Delay-dependent stability criterion for uncertain discrete time systems in presence of actuator saturation (original) (raw)
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International Journal of Automation and Control, 2022
This paper contemplates the H∞ control of discrete-time delayed systems together with actuator saturation, parametric uncertainties and disturbances. H∞-based state feedback controller is conceived to stabilise the closed loop system. Lyapunov Krasovskii functional (LKF), discrete Wirtinger-based summation inequality and convex hull approach are combined to obtain novel regional stability conditions. The estimated attraction domain is maximised using an optimisation method along with linear matrix inequality (LMI). A comparative study is shown between the obtained and existing findings. The results are found to be less conservative than the prior ones. Finally, instances signify efficacy of presented approaches.
Mathematical Problems in Engineering, 2019
This paper examines the stability analysis of discrete-time control systems particularly during the event of actuator saturation and time-varying state delay. With the help of Wirtinger inequality along with Lyapunov-Krasovskii functional gain of state feedback controller is determined for stabilization of above system. The saturation nonlinearity is represented in the terms of convex hull. A new linear matrix inequality (LMI) criterion is settled with reciprocally convex combination based inequality which is dependent on delay. The proposed criterion is less conservative in concern to increase the delay bound and a controller is also simulated for real time problem of missile control system in this paper. It is also attained that projected stability criterion is less conservative compared to other outcomes. Furthermore, an optimization procedure together with LMI constraints has been proposed to maximize the attraction of domain.
ISRN Applied Mathematics, Hindawi, 2014
The problem of global asymptotic stability of a class of uncertain discrete-time systems in the presence of saturation nonlinearities and interval-like time-varying delay in the state is considered. The uncertainties associated with the system parameters are assumed to be deterministic and normbounded. The objective of the paper is to propose stability criteria having considerably smaller numerical complexity. Two new delay-dependent stability criteria are derived by estimating the forward difference of the Lyapunov functional using the concept of reciprocal convexity and method of scale inequality, respectively. The presented criteria are compared with a previously reported criterion. A numerical example is provided to illustrate the effectiveness of the presented criteria.
Analysis and Design of Uncertain Time-Delay Systems Subject to Actuator Saturation
2006 6th World Congress on Intelligent Control and Automation, 2006
This paper is devoted to stability analysis of uncertain continuous-time systems with time-delay in state and input saturation. The domain of attraction of the origin resulting from an a priori designed state feedback law is analyzed using Lyapunov-Razumikhin function approach. Delay-dependent estimation of the domain of attraction is presented using linear matrix inequality (LMI) technique which can be easily used for controller synthesis. The problem of designing linear state feedback laws such that the domain of attraction is enlarged is formulated and solved as an optimization problem with LMI constraints. The effectiveness of the developed method is illustrated with example.
International Journal of Automation and Control, 2023
This paper contemplates the H∞ control of discrete-time delayed systems together with actuator saturation, parametric uncertainties and disturbances. H∞-based state feedback controller is conceived to stabilise the closed loop system. Lyapunov Krasovskii functional (LKF), discrete Wirtinger-based summation inequality and convex hull approach are combined to obtain novel regional stability conditions. The estimated attraction domain is maximised using an optimisation method along with linear matrix inequality (LMI). A comparative study is shown between the obtained and existing findings. The results are found to be less conservative than the prior ones. Finally, instances signify efficacy of presented approaches.
IEEE/CAA Journal of Automatica Sinica, 2020
In this paper, a novel non-monotonic Lyapunov-Krasovskii functional approach is proposed to deal with the stability analysis and stabilization problem of linear discrete time-delay systems. This technique is utilized to relax the monotonic requirement of the Lyapunov-Krasovskii theorem. In this regard, the Lyapunov-Krasovskii functional is allowed to increase in a few steps, while being forced to be overall decreasing. As a result, it relays on a larger class of Lyapunov-Krasovskii functionals to provide stability of a state-delay system. To this end, using the non-monotonic Lyapunov-Krasovskii theorem, new sufficient conditions are derived regarding linear matrix inequalities (LMIs) to study the global asymptotic stability of state-delay systems. Moreover, new stabilization conditions are also proposed for time-delay systems in this article. Both simulation and experimental results on a pH neutralizing process are provided to demonstrate the efficacy of the proposed method.
Delay-Dependent H∞ Control of Uncertain Discrete Delay Systems
European Journal of Control
A delay-dependent solution is given for state-feedback H 1 control of linear discrete-time systems with unknown constant or time-varying delays and with polytopic or norm-bounded uncertainties. Sufficient conditions are obtained for stability and for achieving design specifications which are based on Lyapunov-Krasovskii functionals via a descriptor representation of the system. Similarly to the corresponding continuous-time results these conditions provide an efficient tool for analysis and synthesis of linear systems with time delay. The advantage of the new approach is demonstrated via a simple example.
H∞ Control of Distributed and Discrete Delay Systems via Discretized Lyapunov Functional
European Journal of Control, 2009
The discretized Lyapunov functional method is extended to linear systems with both, discrete and distributed delays, and to H1 control. The coefficients associated with the distributed delay are assumed to be piecewise constant. A new Bounded Real Lemma (BRL) is derived in terms of Linear Matrix Inequalities (LMIs) via descriptor approach. In three numerical examples considered for retarded type systems, the resulting values of H1-norm converge to the exact ones. The analysis results are applied to state-feedback H1 control of linear neutral systems with discrete and distributed delays, where the controller may be either instantaneous or may contain discrete or distributed delay terms. A numerical example illustrates the efficiency of the design method and the advantage of using distributed delay term in the feedback for H1 control of systems with state delay.
IEEE Transactions on Automatic Control, 2018
We address the problem of robust input-to-state stabilization of parameter-varying discrete-time systems with time-varying state delay, saturating actuators, and subject to ℓ2-limited disturbance. It is assumed that the delay belongs to a known interval and its maximum variation between two consecutive instants is taken into account. The proposed convex delay-dependent conditions for the synthesis of robust state feedback controllers ensure local input-to-state stability of the closed-loop system for a set of initial conditions and for energy bounded disturbance signals. However, the computed controllers do not require the real-time knowledge of the delay. The approach is based on the rewriting of the saturating and delayed system in terms of a switched uncertain augmented delay-free system with a dead-zone non-linearity and on the application of the generalized sector condition. To illustrate the efficiency of our approach, we compare it by means of numerical examples with others found in the literature.
Proceedings of the 19th IFAC World Congress, 2014
In this paper the problem of local stabilization of nonlinear discrete-time systems with time-varying delay and saturating actuators is studied. Firstly, through a fuzzy Lyapunov-Krasovskii (L-K) function, we develop convex conditions to synthesize fuzzy state feedback gain controllers that stabilize the nonlinear system subject to saturating actuators. Next, we introduce a new approach to compute an estimate of the region of attraction where the initial condition sequence is split into two subsequences. The first one is composed of the state vector at the actual instant of sampling, i.e. for k = 0. The second one is composed of the state vectors at the delayed samplings. Then, we propose a convex optimization problem to maximize the estimated region of attraction of the closed loop control system. Finally, we give a numerical example to illustrate the obtained results.