Robust ℋ℞ filter design for polytopic linear discrete-time delay systems via LMIs and polynomial matrices (original) (raw)
2011
This paper presents new robust linear matrix inequality conditions for full order robust H ∞ filter design of discrete-time polytopic linear systems affected by a timevarying delay. Thanks to the use of a larger number of slack variables, the proposed conditions are less conservative than the existing methods. Numerical experiments illustrate the better performance of the proposed filter design procedure when compared to other approaches available in the literature.
IET Control Theory & Applications, 2013
This paper presents new robust linear matrix inequality (LMI) conditions for robust H ∞ full order filter design of discrete-time linear systems affected by time-invariant uncertainty and a time-varying state delay. Thanks to the use of a larger number of slack variables, the proposed robust LMI conditions contain and generalize other results from the literature. LMI relaxations based on homogeneous polynomial matrices of arbitrary degree are used to determine the state space realization of the full order filter, that can also be implemented with delayed state terms whenever the timedelay is available in real time. As another contribution, an iterative LMI-based procedure involving the decision variables is proposed to improve the H ∞ filter performance. Numerical experiments illustrate the better performance of the proposed filter when compared to other approaches available in the literature. −d 2 Z 1 (α) − δ 2 Q 4 (α) − d 2 Z 2 (α)
Robust ℋ2 filter design for polytopic linear systems via LMIs and polynomial matrices
2010
This paper presents new linear matrix inequality conditions for full order robust H 2 filter design for continuous and discrete-time polytopic linear systems with time-invariant uncertainty. Thanks to the use of a larger number of slack variables, the proposed conditions are less conservative than the existing conditions in the literature, containing recently published results as particular cases. Examples illustrate the better performance of the proposed filters when compared to other approaches for robust filter design.
An input–output approach to H∞ reduced filter design for polytopic time-varying delay systems
International Journal of Systems Science, 2018
This paper discusses the problem of delay-dependent robust H ∞ filtering design for polytopic systems with a time-varying delay. A new model transformation is firstly applied by employing a three-term approximation for the delayed state, which leads to a smaller approximation error than the two-term approximation. Then, based on the scaled small-gain Theorem combined with an appropriate Lyapunov-Krasovskii Functional, the H ∞ performance analysis of the filtering error system is examined and then the H ∞ full-and reduced-order filters are designed in terms of linear matrix inequalities via a simple linearisation technique. Before the end, a sufficient condition is presented to solve the problem of H ∞ filtering design for a time-delay system without polytopic uncertainties. Finally, illustrative examples are presented to demonstrate the validity of the proposed methods.
Journal of the Franklin Institute, 2011
Convex conditions, expressed as linear matrix inequalities (LMIs), for stability analysis and robust design of uncertain discrete-time systems with time-varying delay are presented in this paper. Delaydependent and delay-independent convex conditions are given. This paper is particularly devoted to the synthesis case where convex conditions are proposed to consider maximum allowed delay interval. It is also presented some relaxed LMIs that yield less conservative conditions at the expense of increasing the computational burden. Extensions to cope with decentralized control and output feedback control are discussed. Numerical examples, including real world motivated models, are presented to illustrate the effectiveness of the proposed approach. (V.J.S. Leite). constant delay. The problem of robust filtering for discrete-time uncertain systems with delayed states is considered in some papers. Delayed state systems with norm-bounded uncertainties are studied in and with polytopic uncertainties in . In the last case the delay is time-invariant. Recently, the problem of output feedback has attracted attention and can be cited as examples of on going research. In special, presents results for precisely known systems with time-varying delay including both static output feedback (SOF) and dynamic output feedback. The conditions, however, are presented as an interactive method that relax some matrix inequalities. In time-varying delay is assumed and a nonlinear algorithm is proposed to obtain a stabilizing controller. In [24] the results of [11] are extended, including polytopic uncertainties and constant Lyapunov-Krasovskii matrices. An interesting application can be found in the context of network control system: although most of the studies in the literature on this subject deal with continuous-time models, nowadays there are some approaches using discrete-time models with delayed states . See also for a robust adaptive sliding mode control scheme applied to discrete-time systems with time-varying delay in the state and subject to norm-bounded uncertainties. In the context of discrete-time-varying systems with time-varying delay in the state, see for convex approaches to the dynamic output feedback controller design problem.
Delay-Dependent Robust H ∞ Filter Design for Uncertain Linear Systems with Time-Varying Delay
Circuits, Systems & Signal Processing, 2009
A new delay-dependent robust H ∞ filtering design for uncertain linear systems with time-varying delay is investigated. Two kinds of time-varying delays are considered. One is differentiable uniformly bounded with a bounded delay derivative; the other is continuous uniformly bounded. A full-order filter is designed which ensures the asymptotic stability of the filtering error system and a prescribed level of H ∞ performance for all possible parameters which reside in a given polytope. By constructing a new Lyapunov functional which contains a triple integral term, new delay-dependent conditions for the existence of the H ∞ filter are derived which are less conservative than the existing ones. The filter gain can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, two numerical examples are given to show the effectiveness and the advantages of the proposed method.
Robust stabilization of polytopic discrete-time systems with time-varying delay in the states
49th IEEE Conference on Decision and Control (CDC), 2010
Convex conditions, expressed as linear matrix inequalities (LMIs), for stability analysis and robust design of uncertain discrete-time systems with time-varying delay are presented in this paper. Delaydependent and delay-independent convex conditions are given. This paper is particularly devoted to the synthesis case where convex conditions are proposed to consider maximum allowed delay interval. It is also presented some relaxed LMIs that yield less conservative conditions at the expense of increasing the computational burden. Extensions to cope with decentralized control and output feedback control are discussed. Numerical examples, including real world motivated models, are presented to illustrate the effectiveness of the proposed approach. (V.J.S. Leite). constant delay. The problem of robust filtering for discrete-time uncertain systems with delayed states is considered in some papers. Delayed state systems with norm-bounded uncertainties are studied in and with polytopic uncertainties in . In the last case the delay is time-invariant. Recently, the problem of output feedback has attracted attention and can be cited as examples of on going research. In special, presents results for precisely known systems with time-varying delay including both static output feedback (SOF) and dynamic output feedback. The conditions, however, are presented as an interactive method that relax some matrix inequalities. In time-varying delay is assumed and a nonlinear algorithm is proposed to obtain a stabilizing controller. In [24] the results of [11] are extended, including polytopic uncertainties and constant Lyapunov-Krasovskii matrices. An interesting application can be found in the context of network control system: although most of the studies in the literature on this subject deal with continuous-time models, nowadays there are some approaches using discrete-time models with delayed states . See also for a robust adaptive sliding mode control scheme applied to discrete-time systems with time-varying delay in the state and subject to norm-bounded uncertainties. In the context of discrete-time-varying systems with time-varying delay in the state, see for convex approaches to the dynamic output feedback controller design problem.
Robust H∞ filter design for uncertain linear systems with multiple time-varying state delays
IEEE Transactions on Signal Processing, 2001
The problem of robust H∞ filtering for continuous-time uncertain linear systems with multiple time-varying delays in the state variables is investigated. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. The aim is to design a stable linear filter assuring asymptotic stability and a prescribed H∞ performance level for the filtering error system, irrespective of the uncertainties and the time delays. Sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities, which can be efficiently solved by means of powerful convex programming tools with global convergence assured. An example illustrates the proposed methodology
Robust Stabilization of Discrete-Time Systems with Time-Varying Delay: An LMI Approach
Mathematical Problems in Engineering, 2008
Sufficient linear matrix inequality LMI conditions to verify the robust stability and to design robust state feedback gains for the class of linear discrete-time systems with time-varying delay and polytopic uncertainties are presented. The conditions are obtained through parameter-dependent Lyapunov-Krasovskii functionals and use some extra variables, which yield less conservative LMI conditions. Both problems, robust stability analysis and robust synthesis, are formulated as convex problems where all system matrices can be affected by uncertainty. Some numerical examples are presented to illustrate the advantages of the proposed LMI conditions.
International Journal of Automation and Smart Technology, 2016
This paper presents new delay-dependent robust linear matrix inequality (LMI) conditions for a robust H ∞ filter for discrete time systems affected by time-varying state delays and missing measurements. Our attention is focused on the analysis and design of robust H ∞ filters. LMI relaxations based on homogeneous polynomial matrices of an arbitrary degree are used to determine the state-space realization of the filter. The missing measurements are described by a binary switching sequence satisfying a Bernoulli distribution. Numerical examples are presented to illustrate the effectiveness and applicability of the proposed method.
Robust ℋ∞ filtering for uncertain discrete-time state-delayed systems
IEEE Transactions on Signal Processing, 2001
This paper addresses the problem of robust ℋ∞ filtering for linear discrete-time systems subject to parameter uncertainties in the system state-space model and with multiple time delays in the state variables. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. A methodology is developed to design a stable linear filter that assures asymptotic stability and a prescribed ℋ∞ performance for the filtering error, irrespective of the uncertainty and the time delays. The proposed design is given in terms of linear matrix inequalities, which has the advantage in that it can be implemented numerically very efficiently
Robust H∞ filtering for uncertain discrete-time state-delayed systems
IEEE Transactions on Signal Processing, 2001
This paper addresses the problem of robust filtering for linear discrete-time systems subject to parameter uncertainties in the system state-space model and with multiple time delays in the state variables. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. A methodology is developed to design a stable linear filter that assures asymptotic stability and a prescribed performance for the filtering error, irrespective of the uncertainty and the time delays. The proposed design is given in terms of linear matrix inequalities, which has the advantage in that it can be implemented numerically very efficiently.
New filter design for linear time-delay systems
Linear Algebra and its Applications, 2011
This paper develops new robust delay-dependent filter design for a class of linear systems with time-varying delays and convexbounded parameter uncertainties. The design procedure hinges upon the constructive use of an appropriate Lyapunov functional plus a free-weighting matrices in order to exhibit the delaydependent dynamics. The developed approach utilizes smaller number of LMI decision variables thereby leading to less conservative solutions to the delay-dependent stability and filtering problems. Subsequently, linear matrix inequalities (LMIs)-based conditions are characterized such that the linear delay system is robustly asymptotically stable with an γ -level L 2 -gain. All the developed results are tested on representative examples.
Robust filter design for piecewise discrete-time systems with time-varying delays
International Journal of Robust and Nonlinear Control, 2009
A novel delay-dependent filtering design approach is developed for a class of linear piecewise discrete-time systems with convex-bounded parametric uncertainties and time-varying delays. The time-delays appear in the state as well as the output and measurement channels. The filter has a linear full-order structure and guarantees the desired estimation accuracy over the entire uncertainty polytope. The desired accuracy is assessed in terms of either H ∞ -performance or L 2 -L ∞ criteria. A new parametrization procedure based on a combined Finsler's Lemma and piecewise Lyapunov-Krasovskii functional is established to yield sufficient conditions for delay-dependent filter feasibility. The filter gains are determined by solving a convex optimization problem over linear matrix inequalities. In comparison to the existing design methods, the developed methodology yields the least conservative measures since all previous overdesign limitations are almost eliminated. By means of simulation examples, the advantages of the developed technique are readily demonstrated.
Robust ℋ/sub ∞/ filtering for uncertain discrete-time state-delayed systems
IEEE Transactions on Signal Processing, 2001
This paper addresses the problem of robust filtering for linear discrete-time systems subject to parameter uncertainties in the system state-space model and with multiple time delays in the state variables. The uncertain parameters are supposed to belong to a given convex bounded polyhedral domain. A methodology is developed to design a stable linear filter that assures asymptotic stability and a prescribed performance for the filtering error, irrespective of the uncertainty and the time delays. The proposed design is given in terms of linear matrix inequalities, which has the advantage in that it can be implemented numerically very efficiently.
Robust filtering for a class of uncertain linear systems with time-varying delay
Automatica, 2008
This paper deals with the problem of delay-dependent robust H ∞ filtering for uncertain linear systems with time-varying delay. Two cases of time-varying delays are fully considered; one is the time-varying delay being continuous uniformly bounded while the other is the time-varying delay being differentiable uniformly bounded with delay-derivative bounded by a constant. A stable linear filter is designed to ensure that the filtering error system is asymptotically stable with a prescribed level of H ∞ noise attenuation. Based on a new integral inequality, delaydependent sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities (LMIs). Through deriving these conditions, neither model transformation nor bounding technique for cross terms is employed. Moreover, the relationship between the sufficient conditions for the two cases of time-varying delay is disclosed. Finally, two examples are also given to illustrate the effectiveness of the proposed methodology. ᭧
Optimal Control Applications & Methods, 2016
This paper deals with the problem of finite frequency H 1 full-order filter design for discrete-time and continuous-time linear systems, with polytopic uncertainties. Based on the generalized Kalman-Yakubovich-Popov lemma and a parameter-dependent Lyapunov function, a set of sufficient conditions are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the H 1 attenuation level, from disturbance to the estimation error, is smaller than a given value over a prescribed finite frequency domain of the external disturbances. Then, in order to linearize and relax the obtained matrix inequalities, we introduce a large number of slack variables by applying Finsler's lemma twice, which provides extra degrees of freedom in optimizing the guaranteed H 1 performance. This leads to performance improvement and reduction of conservatism in the solution. It is shown later that the robust filter gains can be obtained by solving a set of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed approach in comparison with the existing methods.
Robust stability of time-delay continuous-time systems in polytopic domains
2003
Most of the existent linear matrix inequality based conditions for robust stability of time-delay systems in polytopic domains are expressed in terms of constant Lyapunov-Krasovskii functions. This note presents a simple way to extend these conditions in order to construct parameter-dependent functions that provide less conservative results, in both delay-independent and delay-dependent situations.
International Journal of Dynamics and Control, 2023
This paper deals with the problem of delay-dependent robust H ∞ filtering for uncertain two-dimensional (2-D) continuous systems described by Roesser state space model with time-varying delays, with the uncertain parameters assumed to be of polytopic type. A sufficient condition for H ∞ noise attenuation is derived in terms of linear matrix inequalities, so a robust H ∞ filter can be obtained by solving a convex optimization problem. Finally, some examples are provided to illustrate the effectiveness of the proposed methodology. Keywords 2-D continuous systems • Uncertainty • Delayed states • H ∞ filtering • Linear matrix inequality (LMI) This work is funded by AECI AP/034911/11 and MiCInn DPI2010-21589-c05.