Reinaldo M Palhares | Federal University of Minas Gerais (original) (raw)

Papers by Reinaldo M Palhares

Research paper thumbnail of Evolving Fuzzy System Applied to Battery Charge Capacity Prediction for Fault Prognostics

Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)

This paper addresses the use of data-driven evolving techniques applied to fault prognostics. In ... more This paper addresses the use of data-driven evolving techniques applied to fault prognostics. In such problems, accurate predictions of multiple steps ahead are essential for the Remaining Useful Life (RUL) estimation of a given asset. The fault prognostics' solutions must be able to model the typical nonlinear behavior of the degradation processes of these assets, and be adaptable to each unit's particularities. In this context, the Evolving Fuzzy Systems (EFSs) are models capable of representing such behaviors, in addition of being able to deal with nonstationary behavior, also present in these problems. Moreover, a methodology to recursively track the model's estimation error is presented as a way to quantify uncertainties that are propagated in the long-term predictions. The wellestablished NASA's Li-ion batteries data set is used to evaluate the models. The experiments indicate that generic EFSs can take advantage of both historical and stream data to estimate the RUL and its uncertainty.

Research paper thumbnail of Controle robusto de horizonte finito em sistemas lineares com parâmetros variantes no tempo e saltos Markovianos

Anais do 14º Simpósio Brasileiro de Automação Inteligente

This paper presents a strategy to calculate a suboptimal solution to the finite-time linear-quadr... more This paper presents a strategy to calculate a suboptimal solution to the finite-time linear-quadratic control problem of Markov jump linear systems. When the mode is fixed, the system has parameter-varying matrices that take values in a polutopic set. An upper bound for the cost function is obtained and, as a consequence, the feedback gains are calculated by solving an optimization problem written in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed method. Resumo: Este trabalho apresenta uma estratégia para calcular uma solução subótima para o problema de controle linear quadrático de tempo finito de sistemas lineares com saltos Markovianos. Quando os modos são fixados, o sistema tem matrizes com parâmetros variantes, os quais tomam valores em um conjunto politópico. Um limitante superior para a função custoé obtido, como consequência, os ganhos de realimentação são calculados resolvendo um problema de otimização escrito em termos de desigualdades matriciais lineares. Um exemplo numéricoé dado para ilustrar a eficácia do método proposto.

Research paper thumbnail of Avoiding the matrix inversion in Takagi-Sugeno-based advanced controllers and observers

IEEE Transactions on Fuzzy Systems

Research paper thumbnail of Monitoring the Stator Current in Induction Machines for Possible Fault Detection: A Fuzzy/Bayesian Approach for the Problem of Time Series Multiple Change Point Detection

Pesquisa Operacional

This paper addresses the problem of fault detection in stator winding of induction machine by a m... more This paper addresses the problem of fault detection in stator winding of induction machine by a multiple change points detection approach in time series. To handle this problem a new fuzzy/Bayesian approach is proposed which differs from previous approaches since it does not require prior information as: the number of change points or the characterization of the data probabilistic distribution. The approach has been applied in the monitoring the current of the stator winding induction machine. The good results obtained by proposed methodology illustrate its efficiency.

Research paper thumbnail of Advanced model based air path management using a discrete-angular controller in idle-speed context

Research paper thumbnail of LMI-based control synthesis of constrained Takagi–Sugeno fuzzy systems subject to L 2 or L ∞ disturbances

Research paper thumbnail of Special issue on recent advances on control and diagnosis via process measurements

Journal of the Franklin Institute, 2017

Research paper thumbnail of Formal Non-Fragile Stability Verification of Digital Control Systems with Uncertainty

IEEE Transactions on Computers, 2016

A verification methodology is described and evaluated to formally determine uncertain linear syst... more A verification methodology is described and evaluated to formally determine uncertain linear systems stability in digital controllers with considerations to the implementation aspects. In particular, this methodology is combined with the digital-system verifier (DSVerifier), which is a verification tool that employs Bounded Model Checking based on Satisfiability Modulo Theories to check the stability of digital control systems with uncertainty. DSVerifier determines the control system stability, considering all the plant interval variation set, together with the Finite Word-length (FWL) effects in the digital controller implementation; DSVerifier checks the robust non-fragile stability of a given closed-loop system. The proposed methodology and respective tool are evaluated considering non-fragile control examples from literature. Experimental results show that the approach used in this study is able to foresee fragility problems in robust controllers, which could be overlooked by other existing approaches due to underestimating of FWL effects.

Research paper thumbnail of Counterpart of Advanced TS discrete controller without matrix inversion

Research paper thumbnail of Multiobjective optimization applied to robust /spl Hscr//sub 2///spl Hscr//sub /spl infin// state-feedback control synthesis

Proceedings of the 2004 American Control Conference, 2004

This paper presents an algorithm for robust H2/H∞ state-feedback control synthesis, with regional... more This paper presents an algorithm for robust H2/H∞ state-feedback control synthesis, with regional pole placement, based on a multiobjective optimization algorithm with non-smooth problem-solving capability. The problem is formulated with the state-feedback matrix coefficients as optimization parameters. The closed-loop performance obtained by means of the proposed strategy is assessed for the whole uncertainty-set through an LMI-based H2 and H∞ guaranteed cost computation. The proposed strategy is compared with three former LMI approaches, for systems with polytope-bounded uncertainties, and presents better results.

Research paper thumbnail of Discussion on Continuous-time periodic H-infinity filtering via LMI

European Journal of Control, May 12, 2001

Research paper thumbnail of New delay-interval stability condition

Http Dx Doi Org 10 1080 00207721 2012 720297, Sep 23, 2013

The delay-dependent stability problem for systems with time-delay varying in an interval is addre... more The delay-dependent stability problem for systems with time-delay varying in an interval is addressed in this article. The new idea in this article is to connect two very efficient approaches: the discretised Lyapunov functional for systems with pointwise delay and the convex analysis for systems with time-varying delay. The proposed method is able to check the stability interval when the time-varying delay d(t) belongs to an interval [r, ]. The case of unstable delayed systems for r ¼ 0 is also treatable. The resulting criterion, expressed in terms of a convex optimisation problem, outperforms the existing ones in the literature, as illustrated by the numerical examples.

Research paper thumbnail of New Lyapunov Function and Extra Information on Membership Functions for Improving Stability Conditions of TS Systems

This paper presents an improved stability condition for Takagi-Sugeno (TS) fuzzy systems based on... more This paper presents an improved stability condition for Takagi-Sugeno (TS) fuzzy systems based on a new fuzzy Lyapunov function. This new fuzzy Lyapunov function aggregates more information with respect to the membership function variation (time-derivative) via an augmented state vector. This new fuzzy Lyapunov function is not just parametrized by the membership functions variations but it is also based on a polynomial combination of them. To derive LMI based stability condition using the proposed new fuzzy Lyapunov function two ideas are invoked: i) the inclusion of the membership function time-derivative information using a finite number of vectors and, ii) the use of the so-called null term. Two numerical examples are presented to illustrate the improvements.

Research paper thumbnail of Stability analysis of Takagi-Sugeno fuzzy systems via LMI: methodologies based on a new fuzzy Lyapunov function

Sba: Controle & Automação Sociedade Brasileira de Automatica, 2011

Stability analysis of TS fuzzy systems can be much improved by resorting to fuzzy Lyapunov functi... more Stability analysis of TS fuzzy systems can be much improved by resorting to fuzzy Lyapunov functions, since they are parameterized by membership functions and can better characterize the time-varying feature of these systems by means of the information regarding the first time-derivative of the membership functions. In this paper an enhanced fuzzy Lyapunov function is used to develop stability conditions that evaluate also the second time-derivative of membership functions, improving the time-varying characterization of TS systems. By using diferent strategies to consider the information regarding such derivatives and employing some numerical tools that decouple system from Lyapunov function matrices new LMI tests are developed. Numerical examples illustrate the effectiveness of those methodologies.

Research paper thumbnail of Alternative LMIs characterization of ℋ/sub 2/ and central ℋ/sub ∞/ discrete-time controllers

Proceedings of 35th IEEE Conference on Decision and Control, 1996

This paper proposes alternative LMIs characterization for the 'HZ and the central 'H~state feedba... more This paper proposes alternative LMIs characterization for the 'HZ and the central 'H~state feedback controllers for discrete-time systems, allowing the immediate extension to handle uncertain systems belonging to convex polyhedral domains.

Research paper thumbnail of Fault detection in dynamic systems by a Fuzzy/Bayesian network formulation

Applied Soft Computing, 2014

ABSTRACT In this paper the fault detection problem is solved using an alternative methodology bas... more ABSTRACT In this paper the fault detection problem is solved using an alternative methodology based on a fuzzy/Bayesian strategy combining a Bayesian network and the fuzzy set theory. The new important issue in this proposed methodology is to address uncertainties in the input of the Bayesian Network. This contribution is possible since the fuzzy set theory is used as the knowledge representation. To illustrate the technique, the fault detection problem in induction machine stator-winding is considered. Specifically, the faults in the induction machine stator-winding are detected by a state change of stator current. Simulation results are presented to illustrate the advance of the proposed methodology when compared to standard Bayesian network.

Research paper thumbnail of Using information on membership function shapes in asymptotically exact triangulation approaches

2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012

Many Takagi-Sugeno (TS) synthesis and analysis conditions can be expressed as positive/negative d... more Many Takagi-Sugeno (TS) synthesis and analysis conditions can be expressed as positive/negative definiteness conditions of fuzzy summations. In this regard, several sufficient conditions have been proposed in the literature that are asymptotically exact (i.e. necessary and sufficient as their number tends to infinity). However, since these conditions do not take the membership function shapes into account (aside from the fact that they add up to one and are greater than zero), the exactness of these conditions is only true when the membership functions can assume any possible combination of values inside the standard simplex. By making use of the membership functions shapes, in this paper we propose a triangulation (or simplicial partition) based approach that generates asymptotically exact conditions for fuzzy summations with a possibly smaller growing rate of added simplices per iteration than that observed in recently published algorithms. The set of conditions are Linear Matrix Inequalities (LMIs), for which efficient numerical routines are available.

Research paper thumbnail of On delay-dependent stability conditions for Takagi–Sugeno fuzzy systems

Journal of the Franklin Institute, 2013

ABSTRACT This paper presents new less conservative stability analysis conditions for Takagi–Sugen... more ABSTRACT This paper presents new less conservative stability analysis conditions for Takagi–Sugeno fuzzy systems subject to interval time-varying delay. The methodology is based on the direct Lyapunov method allied with an appropriate Lyapunov–Krasovskii functional choice and the use of the integral inequalities, Finsler lemma, Newton–Leibniz formula manipulations and convex combination properties. Particularly, the main result differs from previous ones since the positiveness of the Lyapunov–Krasovskii functional is guaranteed by new relaxed conditions. Two examples illustrate the effectiveness of the proposed methodology.

Research paper thumbnail of New delay-interval stability condition

International Journal of Systems Science, 2014

The delay-dependent stability problem for systems with time-delay varying in an interval is addre... more The delay-dependent stability problem for systems with time-delay varying in an interval is addressed in this article. The new idea in this article is to connect two very efficient approaches: the discretised Lyapunov functional for systems with pointwise delay and the convex analysis for systems with time-varying delay. The proposed method is able to check the stability interval when the time-varying delay d(t) belongs to an interval [r, ]. The case of unstable delayed systems for r ¼ 0 is also treatable. The resulting criterion, expressed in terms of a convex optimisation problem, outperforms the existing ones in the literature, as illustrated by the numerical examples.

Research paper thumbnail of Synchronizing Continuous Time Chaotic Systems Over Nondeterministic Networks with Packet Dropouts

International Journal of Bifurcation and Chaos, 2012

The problem of control synthesis for master–slave synchronization of continuous time chaotic syst... more The problem of control synthesis for master–slave synchronization of continuous time chaotic systems of Lur'e type using sampled feedback control subject to sampling time random fluctuation and data packet dropouts is investigated. New stability and stabilization conditions are proposed based on Linear Matrix Inequalities (LMIs). The idea is to connect two very efficient approaches to deal with delayed systems: the discretized Lyapunov functional for systems with pointwise delay and the convex analysis for systems with time-varying delay. Simulation examples based on synchronizing coupled Chua's circuits are used to illustrate the effectiveness of the proposed methodology.

Research paper thumbnail of Evolving Fuzzy System Applied to Battery Charge Capacity Prediction for Fault Prognostics

Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)

This paper addresses the use of data-driven evolving techniques applied to fault prognostics. In ... more This paper addresses the use of data-driven evolving techniques applied to fault prognostics. In such problems, accurate predictions of multiple steps ahead are essential for the Remaining Useful Life (RUL) estimation of a given asset. The fault prognostics' solutions must be able to model the typical nonlinear behavior of the degradation processes of these assets, and be adaptable to each unit's particularities. In this context, the Evolving Fuzzy Systems (EFSs) are models capable of representing such behaviors, in addition of being able to deal with nonstationary behavior, also present in these problems. Moreover, a methodology to recursively track the model's estimation error is presented as a way to quantify uncertainties that are propagated in the long-term predictions. The wellestablished NASA's Li-ion batteries data set is used to evaluate the models. The experiments indicate that generic EFSs can take advantage of both historical and stream data to estimate the RUL and its uncertainty.

Research paper thumbnail of Controle robusto de horizonte finito em sistemas lineares com parâmetros variantes no tempo e saltos Markovianos

Anais do 14º Simpósio Brasileiro de Automação Inteligente

This paper presents a strategy to calculate a suboptimal solution to the finite-time linear-quadr... more This paper presents a strategy to calculate a suboptimal solution to the finite-time linear-quadratic control problem of Markov jump linear systems. When the mode is fixed, the system has parameter-varying matrices that take values in a polutopic set. An upper bound for the cost function is obtained and, as a consequence, the feedback gains are calculated by solving an optimization problem written in terms of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed method. Resumo: Este trabalho apresenta uma estratégia para calcular uma solução subótima para o problema de controle linear quadrático de tempo finito de sistemas lineares com saltos Markovianos. Quando os modos são fixados, o sistema tem matrizes com parâmetros variantes, os quais tomam valores em um conjunto politópico. Um limitante superior para a função custoé obtido, como consequência, os ganhos de realimentação são calculados resolvendo um problema de otimização escrito em termos de desigualdades matriciais lineares. Um exemplo numéricoé dado para ilustrar a eficácia do método proposto.

Research paper thumbnail of Avoiding the matrix inversion in Takagi-Sugeno-based advanced controllers and observers

IEEE Transactions on Fuzzy Systems

Research paper thumbnail of Monitoring the Stator Current in Induction Machines for Possible Fault Detection: A Fuzzy/Bayesian Approach for the Problem of Time Series Multiple Change Point Detection

Pesquisa Operacional

This paper addresses the problem of fault detection in stator winding of induction machine by a m... more This paper addresses the problem of fault detection in stator winding of induction machine by a multiple change points detection approach in time series. To handle this problem a new fuzzy/Bayesian approach is proposed which differs from previous approaches since it does not require prior information as: the number of change points or the characterization of the data probabilistic distribution. The approach has been applied in the monitoring the current of the stator winding induction machine. The good results obtained by proposed methodology illustrate its efficiency.

Research paper thumbnail of Advanced model based air path management using a discrete-angular controller in idle-speed context

Research paper thumbnail of LMI-based control synthesis of constrained Takagi–Sugeno fuzzy systems subject to L 2 or L ∞ disturbances

Research paper thumbnail of Special issue on recent advances on control and diagnosis via process measurements

Journal of the Franklin Institute, 2017

Research paper thumbnail of Formal Non-Fragile Stability Verification of Digital Control Systems with Uncertainty

IEEE Transactions on Computers, 2016

A verification methodology is described and evaluated to formally determine uncertain linear syst... more A verification methodology is described and evaluated to formally determine uncertain linear systems stability in digital controllers with considerations to the implementation aspects. In particular, this methodology is combined with the digital-system verifier (DSVerifier), which is a verification tool that employs Bounded Model Checking based on Satisfiability Modulo Theories to check the stability of digital control systems with uncertainty. DSVerifier determines the control system stability, considering all the plant interval variation set, together with the Finite Word-length (FWL) effects in the digital controller implementation; DSVerifier checks the robust non-fragile stability of a given closed-loop system. The proposed methodology and respective tool are evaluated considering non-fragile control examples from literature. Experimental results show that the approach used in this study is able to foresee fragility problems in robust controllers, which could be overlooked by other existing approaches due to underestimating of FWL effects.

Research paper thumbnail of Counterpart of Advanced TS discrete controller without matrix inversion

Research paper thumbnail of Multiobjective optimization applied to robust /spl Hscr//sub 2///spl Hscr//sub /spl infin// state-feedback control synthesis

Proceedings of the 2004 American Control Conference, 2004

This paper presents an algorithm for robust H2/H∞ state-feedback control synthesis, with regional... more This paper presents an algorithm for robust H2/H∞ state-feedback control synthesis, with regional pole placement, based on a multiobjective optimization algorithm with non-smooth problem-solving capability. The problem is formulated with the state-feedback matrix coefficients as optimization parameters. The closed-loop performance obtained by means of the proposed strategy is assessed for the whole uncertainty-set through an LMI-based H2 and H∞ guaranteed cost computation. The proposed strategy is compared with three former LMI approaches, for systems with polytope-bounded uncertainties, and presents better results.

Research paper thumbnail of Discussion on Continuous-time periodic H-infinity filtering via LMI

European Journal of Control, May 12, 2001

Research paper thumbnail of New delay-interval stability condition

Http Dx Doi Org 10 1080 00207721 2012 720297, Sep 23, 2013

The delay-dependent stability problem for systems with time-delay varying in an interval is addre... more The delay-dependent stability problem for systems with time-delay varying in an interval is addressed in this article. The new idea in this article is to connect two very efficient approaches: the discretised Lyapunov functional for systems with pointwise delay and the convex analysis for systems with time-varying delay. The proposed method is able to check the stability interval when the time-varying delay d(t) belongs to an interval [r, ]. The case of unstable delayed systems for r ¼ 0 is also treatable. The resulting criterion, expressed in terms of a convex optimisation problem, outperforms the existing ones in the literature, as illustrated by the numerical examples.

Research paper thumbnail of New Lyapunov Function and Extra Information on Membership Functions for Improving Stability Conditions of TS Systems

This paper presents an improved stability condition for Takagi-Sugeno (TS) fuzzy systems based on... more This paper presents an improved stability condition for Takagi-Sugeno (TS) fuzzy systems based on a new fuzzy Lyapunov function. This new fuzzy Lyapunov function aggregates more information with respect to the membership function variation (time-derivative) via an augmented state vector. This new fuzzy Lyapunov function is not just parametrized by the membership functions variations but it is also based on a polynomial combination of them. To derive LMI based stability condition using the proposed new fuzzy Lyapunov function two ideas are invoked: i) the inclusion of the membership function time-derivative information using a finite number of vectors and, ii) the use of the so-called null term. Two numerical examples are presented to illustrate the improvements.

Research paper thumbnail of Stability analysis of Takagi-Sugeno fuzzy systems via LMI: methodologies based on a new fuzzy Lyapunov function

Sba: Controle & Automação Sociedade Brasileira de Automatica, 2011

Stability analysis of TS fuzzy systems can be much improved by resorting to fuzzy Lyapunov functi... more Stability analysis of TS fuzzy systems can be much improved by resorting to fuzzy Lyapunov functions, since they are parameterized by membership functions and can better characterize the time-varying feature of these systems by means of the information regarding the first time-derivative of the membership functions. In this paper an enhanced fuzzy Lyapunov function is used to develop stability conditions that evaluate also the second time-derivative of membership functions, improving the time-varying characterization of TS systems. By using diferent strategies to consider the information regarding such derivatives and employing some numerical tools that decouple system from Lyapunov function matrices new LMI tests are developed. Numerical examples illustrate the effectiveness of those methodologies.

Research paper thumbnail of Alternative LMIs characterization of ℋ/sub 2/ and central ℋ/sub ∞/ discrete-time controllers

Proceedings of 35th IEEE Conference on Decision and Control, 1996

This paper proposes alternative LMIs characterization for the 'HZ and the central 'H~state feedba... more This paper proposes alternative LMIs characterization for the 'HZ and the central 'H~state feedback controllers for discrete-time systems, allowing the immediate extension to handle uncertain systems belonging to convex polyhedral domains.

Research paper thumbnail of Fault detection in dynamic systems by a Fuzzy/Bayesian network formulation

Applied Soft Computing, 2014

ABSTRACT In this paper the fault detection problem is solved using an alternative methodology bas... more ABSTRACT In this paper the fault detection problem is solved using an alternative methodology based on a fuzzy/Bayesian strategy combining a Bayesian network and the fuzzy set theory. The new important issue in this proposed methodology is to address uncertainties in the input of the Bayesian Network. This contribution is possible since the fuzzy set theory is used as the knowledge representation. To illustrate the technique, the fault detection problem in induction machine stator-winding is considered. Specifically, the faults in the induction machine stator-winding are detected by a state change of stator current. Simulation results are presented to illustrate the advance of the proposed methodology when compared to standard Bayesian network.

Research paper thumbnail of Using information on membership function shapes in asymptotically exact triangulation approaches

2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012

Many Takagi-Sugeno (TS) synthesis and analysis conditions can be expressed as positive/negative d... more Many Takagi-Sugeno (TS) synthesis and analysis conditions can be expressed as positive/negative definiteness conditions of fuzzy summations. In this regard, several sufficient conditions have been proposed in the literature that are asymptotically exact (i.e. necessary and sufficient as their number tends to infinity). However, since these conditions do not take the membership function shapes into account (aside from the fact that they add up to one and are greater than zero), the exactness of these conditions is only true when the membership functions can assume any possible combination of values inside the standard simplex. By making use of the membership functions shapes, in this paper we propose a triangulation (or simplicial partition) based approach that generates asymptotically exact conditions for fuzzy summations with a possibly smaller growing rate of added simplices per iteration than that observed in recently published algorithms. The set of conditions are Linear Matrix Inequalities (LMIs), for which efficient numerical routines are available.

Research paper thumbnail of On delay-dependent stability conditions for Takagi–Sugeno fuzzy systems

Journal of the Franklin Institute, 2013

ABSTRACT This paper presents new less conservative stability analysis conditions for Takagi–Sugen... more ABSTRACT This paper presents new less conservative stability analysis conditions for Takagi–Sugeno fuzzy systems subject to interval time-varying delay. The methodology is based on the direct Lyapunov method allied with an appropriate Lyapunov–Krasovskii functional choice and the use of the integral inequalities, Finsler lemma, Newton–Leibniz formula manipulations and convex combination properties. Particularly, the main result differs from previous ones since the positiveness of the Lyapunov–Krasovskii functional is guaranteed by new relaxed conditions. Two examples illustrate the effectiveness of the proposed methodology.

Research paper thumbnail of New delay-interval stability condition

International Journal of Systems Science, 2014

The delay-dependent stability problem for systems with time-delay varying in an interval is addre... more The delay-dependent stability problem for systems with time-delay varying in an interval is addressed in this article. The new idea in this article is to connect two very efficient approaches: the discretised Lyapunov functional for systems with pointwise delay and the convex analysis for systems with time-varying delay. The proposed method is able to check the stability interval when the time-varying delay d(t) belongs to an interval [r, ]. The case of unstable delayed systems for r ¼ 0 is also treatable. The resulting criterion, expressed in terms of a convex optimisation problem, outperforms the existing ones in the literature, as illustrated by the numerical examples.

Research paper thumbnail of Synchronizing Continuous Time Chaotic Systems Over Nondeterministic Networks with Packet Dropouts

International Journal of Bifurcation and Chaos, 2012

The problem of control synthesis for master–slave synchronization of continuous time chaotic syst... more The problem of control synthesis for master–slave synchronization of continuous time chaotic systems of Lur'e type using sampled feedback control subject to sampling time random fluctuation and data packet dropouts is investigated. New stability and stabilization conditions are proposed based on Linear Matrix Inequalities (LMIs). The idea is to connect two very efficient approaches to deal with delayed systems: the discretized Lyapunov functional for systems with pointwise delay and the convex analysis for systems with time-varying delay. Simulation examples based on synchronizing coupled Chua's circuits are used to illustrate the effectiveness of the proposed methodology.