Stability Of Discrete-time Singular Systems Research Articles

Stability analysis of discrete-time coupled systems with delays

Addressed in this paper is the stability issue of discrete-time delayed coupled systems consisting of a difference equation and an algebraic equation in coupled states. First, a necessary and sufficient condition of exponential stability is proposed for coupled systems with constant delays. Second, periodicity and stability are investigated for periodic coupled systems. Third, based on the Lyapunov inequality, a necessary and sufficient condition is presented for exponential stability of general time-varying coupled systems. Finally, as an application of these results, stability of discrete-time singular systems is discussed.

Robust Admissibilization for Discrete-Time Singular Systems with Time-Varying Delay

The problems of the admissibility and state feedback stabilization for discrete-time singular systems with interval time-varying delay and norm-bounded uncertainty are studied. The system is equivalently transformed into a new comparison form by decomposition. By taking advantage of the Seuret summation inequality, the reciprocally convex inequality, and some relaxation techniques, a delay-dependent criterion that ensures the admissibility of the concerned systems is established. The result on robust stabilization is also obtained by fixing some parameters. It should be pointed out that the results are less dependent on the parameters so that some conservatism is reduced. A numerical example is included to illustrate the effectiveness and improvement of the proposed methods.

이산시간 불확실 특이시스템의 유한시간 강인 산일성 상태궤환 제어기 설계

In this paper, we treat the problem of a robust finite-time dissipative state feedback controller design method for discrete-time singular systems with polytopic uncertainties. A BRL(bounded real lemma) for finite-time stability of discrete-time singular systems is derived. A finite-time dissipative state feedback controller design method satisfying finite-time stability and dissipativity is proposed by LMI(linear matrix inequality) technique on the basis of the obtained BRL. Moreover it is shown that the obtained condition can be extended into polytopic uncertain systems by proper manipulations. Finally, illustrative examples are given to show the applicability of the proposed method.

Stability and stabilization for discrete-time singular systems with infinite distributed delays and actuator failures

In this paper, a reliable H∞ controller is designed for discrete-time singular systems with infinite distributed delays. Firstly, a stability criterion is obtained based on linear matrix inequality (LMI). Then a controller is designed to ensure the singular time-delay system to be regular, causal and stable with disturbance attenuation level γ for possible actuator failures. A numerical example is given to illustrate the validity of the proposed approach.

Robust stabilization for discrete-time nonlinear singular systems with mixed time delays

This paper investigates the robust stability of discrete-time singular systems involving nonlinear disturbance and mixed time delays. The mixed time delays are comprised of both discrete and distributed delays. The interval of discrete time delays can be divided into several subintervals, firstly. Then, in terms of linear matrix inequality (LMI), a suitable state feedback controller is designed for discrete-time singular systems with nonlinear disturbance and mixed time delays, and the overall closed-loop system is regular, causal and mean square asymptotically stable. Numerical examples are provided to show the usefulness and effectiveness of the proposed methods, and the results derived from our approaches are less conservative than existing ones. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society