Persistent Bounded Disturbance Rejection Research Articles

Persistent bounded disturbance rejection for discrete-time delay systems

In this article, we provide a novel solution to the problem of persistent bounded disturbance rejection in linear discrete-time systems with time-varying delays. The solution is developed based on the tools of invariant set analysis and Lyapunov-function method. As an integral part of the solution, we derive less conservative sufficient conditions on robust attractor for discrete-time systems with delays in terms of strict linear matrix inequalities to guarantee the desired ℓ1-performance. A robust state-feedback controller is designed and the associated gain is determined using strict LMIs. The developed results are tested on a representative example.

Persistent bounded disturbance rejection for discrete time-delay systems using output feedback

Persistent bounded disturbance rejection for discrete time-delay systems using output feedback

Rejection of persistent‐bounded disturbances in continuous time‐delay systems using observer‐based feedback

AbstractIn this paper, the problem of persistent‐bounded disturbance rejection of linear continuous‐time systems with time‐varying delays is investigated using the tools of invariant set analysis and Lyapunov‐function methodology. We derive less conservative sufficient conditions on robust attractor for time‐delay systems in terms of strict linear matrix inequalities (LMIs) to guarantee the desired ℒ︁1‐performance. A robust output‐feedback controller is designed and the associated gain is determined using strict LMIs. The developed results are tested on two representative time‐delay examples. Copyright © 2009 John Wiley & Sons, Ltd.

Rejection of Persistent Bounded Disturbance for a Class of Time-Delay Systems

This paper considers the problem of persistent bounded disturbance rejection for a class of time-delay systems by Lyapunov function and positively invariant set analysis method. Sufficient conditions for internal stability and L1–performance analysis are given in terms of linear matrix inequalities (LMIs). Based on which, a dynamic output-feedback controller is then designed. All the obtained results are delay-dependent, and therefore, are less conservative. A numerical example is included to illustrate the proposed method.

An LMI approach to persistent bounded disturbance rejection for a class of nonlinear impulsive systems

The problem of persistent bounded disturbance rejection for a class of nonlinear (Lipschitz-like) impulsive systems is considered through invariant set analysis using the Lyapunov function method. Conditions on a robust attractor for this class of systems are given in terms of linear matrix inequalities (LMIs), which ensure simultaneously internal stability and desired L 1 -performance. The obtained results are only dependent on the Lipschitz-like constant matrices without regard to the nonlinear forms. Based on the results, a simple approach to the design of a robust controller is presented. Finally, a numerical example is worked out to illustrate the efficiency of the theoretical results.

PERSISTENT BOUNDED DISTURBANCE REJECTION FOR IMPULSIVE SYSTEMS WITH PARAMETRIC UNCERTAINTIES: AN LMI APPROACH

The problem of persistent bounded disturbance rejection for linear impulsive systems with parametric uncertainties is considered by Lyapunov function and positively invariant set analysis method. A sufficient condition on robust internal stability and L1-performance of the impulsive systems is established in terms of linear matrix inequalities. Based on this result, a simple approach to design a linear state-feedback controller is presented to stabilize robustly the impulsive systems with uncertainties and to achieve a desired level of disturbance attenuation. A sufficient condition on the existence of a non-fragile state-feedback controller is also obtained. Two numerical examples are worked out to illustrate the feasibility and efficiency of the proposed approach.

Robust Stability and Performance of Uncertain Lurie Systems with State Delays

In this paper, we consider the problem of persistent bounded disturbance rejection for uncertain Lurie systems with delay. We mainly focus on the problems of absolute stability (delay-independent stability and delay-dependent stability) and performance of bounded disturbance rejection using the Lyapunov-Krasovskii function method. In the two cases, we give sufficient conditions for guaranteeing simultaneously absolute stability and achieving certain performance of bounded disturbance rejection in terms of a linear matrix inequality (LMI). For the delay-dependent case, an estimate of the maximum admissible delay bound is established in terms of a generalized eigenvalue problem that can be solved numerically with the efficient LMI toolbox. Similarly, we study the corresponding problem for Lurie delay systems with uncertainties. Finally, two numerical examples are worked out to illustrate the effectiveness of the proposed results.

Persistent bounded disturbance rejection for impulsive systems

The problem of persistent bounded disturbance rejection for impulsive systems is concerned through invariant set analysis using the Lyapunov function method. Conditions on robust attractor for impulsive systems are given in terms of linear matrix inequalities (LMIs), which ensure the desired L/sub 1/-performance. Based on the results, a simple approach to the design of a robust controller is presented. Finally, a numerical example is worked out to illustrate the theoretical results.