Class Of Uncertain Descriptor Systems Research Articles

Robust state-feedback control for discrete-time descriptor systems with norm-bounded parametric uncertainties

ABSTRACTThis paper deals with a state feedback control problem for linear time-invariant discrete-time descriptor systems with norm-bounded parametric uncertainties. To this end, bounded real lemma (BRL) is extended on the class of uncertain descriptor systems. The control design procedure based on the conditions of BRL for uncertain descriptor systems is proposed. Numerical examples are included to illustrate the effectiveness of the present result.

Admissibility analysis and control synthesis for descriptor systems with random abrupt changes

This article addresses the admissibility analysis and state-feedback robust control synthesis problem for a class of uncertain descriptor systems with time delays and Markovian jumping parameters. In particular, the delay factor is assumed to be time varying which belongs to a given interval and parameter uncertainties are assumed to be time-varying but norm bounded. By implementing linear matrix inequality optimization approach together with delay fractioning technique, a new set of delay dependent sufficient condition is derived which guarantees that the uncertain singular system to be regular, impulse-free and stochastically stable. Further, a static robust control design with an appropriate gain control matrix has been derived to achieve the robust stabilization for uncertain singular systems in the presence admissible parameter uncertainties and random abrupt changes. By considering the relationship among the time varying delay and its lower and upper bounds, a new set of sufficient conditions are established for the existence of state feedback control in terms of LMIs, which can be efficiently solved via MATLAB LMI toolbox. More precisely, when these LMIs are feasible, an expression of a desired static robust control will be determined. Further, numerical examples with simulation result are given to show that the obtained result significantly improve the allowable upper bounds of delays over some existing results.

Robust normalization and guaranteed cost control for a class of uncertain descriptor systems

This paper investigates the problem of robust normalization and guaranteed cost control for descriptor systems with uncertainties. The parameter uncertainties are assumed to be time-varying norm-bounded appearing not only in both the state and input matrices but also in the derivative matrix. The quadratic performance index is nonstandard, which includes the additional derivative state term. Attention is focused on the proportional plus derivative state feedback controller design based on the linear matrix inequality method, which guarantees the closed-loop system to be normal and quadratically stable with a prescribed upper bound of the cost function.

Non-fragile PD state [formula omitted] control for a class of uncertain descriptor systems

This paper is concerned with the problem of non-fragile proportional-plus-derivative (PD) state H∞ control for a class of uncertain descriptor systems. The parameter uncertainties are assumed to be time-varying norm-bounded appearing not only in the state matrix but also in the derivative matrix. A new version of bounded real lemma for descriptor systems is proposed, which guarantees a descriptor system to be normal and stable (NS) with γ-disturbance rejection. Based on this, we address the problem of designing non-fragile PD state H∞ controllers with additive and multiplicative controller uncertainties, respectively. Sufficient conditions are presented to synthesize two classes of such non-fragile controllers in terms of LMIs. Finally, a numerical example is provided to illustrate the effectiveness of the proposed design method.

Robust H-infinity fault-tolerant control for uncertain descriptor systems by dynamical compensators

The problem of robust H-infinity fault-tolerant control against sensor failures for a class of uncertain descriptor systems via dynamical compensators is considered. Based on H-infinity theory in descriptor systems, a sufficient condition for the existence of dynamical compensators with H-infinity fault-tolerant function is derived and expressions for the gain matrices in the compensators are presented. The dynamical compensator guarantees that the resultant colsed-loop system is admissible; furthermore, it maintains certain H-infinity norm performance in the normal condition as well as in the event of sensor failures and parameter uncertainties. A numerical example shows the effect of the proposed method.

Robust controllability and robust closed-loop stability with static output feedback for a class of uncertain descriptor systems

This paper considers robust controllability for uncertain linear descriptor systems with structured perturbations. Necessary and sufficient conditions based on the μ-analysis are obtained by transforming the problem into checking the nonsingularity of a class of uncertain matrices. Also a tight bound is obtained in terms of μ for keeping the closed-loop system regular, impulse-free and stable under a preconstructed static output feedback. An example is given to illustrate the results.

Lyapunov stability theory and robust control of uncertain descriptor systems

In this paper we consider the problem of stability and robustness of uncertain nonlinear descriptor systems. The Lyapunov stability theory for conventional systems is extended in a natural way to nonlinear descriptor systems, and some stability theorems for descriptor systems are given. By making use of the stability results developed in this paper, we also discuss the robust control problem of an important class of nonlinear descriptor systems with uncertainties, and propose a class of stabilizing state feedback controllers for this class of uncertain descriptor systems. Finally, a numerical example is given to demonstrate the utilization of our approach.