This note provides an improved asymptotic stability condition for time-delay systems in terms of a strict linear matrix inequality.Unlike previous methods, the mathematical development avoids bounding certain cross terms which often leads to conservatism. When time-varying norm-bounded uncertainties appear in a delay system, an improved robust delay-dependent stability condition is also given. Examples are provided to demonstrate the reduced conservatism of the proposed conditions.

This paper considers the problem of robust H∞ filtering for uncertain two-dimensional (2-D) continuous systems described by the Roesser state-space model. The parameter uncertainties are assumed to be norm-bounded in both the state and measurement equations. The purpose is the design of a 2-D continuous filter such that for all admissible uncertainties, the error system is asymptotically stable, and the H∞ norm of the transfer function, from the noise signal to the estimation error, is below a prespecified level. A sufficient condition for the existence of such filters is obtained in terms of a set of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired H∞ filter is given. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method

This paper investigates the problem of robust output feedback H∞ control for a class of uncertain discrete-time fuzzy systems with time delays. The state-space Takagi–Sugeno fuzzy model with time delays and norm-bounded parameter uncertainties is adopted. The purpose is the design of a full-order fuzzy dynamic output feedback controller which ensures the robust asymptotic stability of the closed-loop system and guarantees an H∞ norm bound constraint on disturbance attenuation for all admissible uncertainties. In terms of linear matrix inequalities (LMIs), a sufficient condition for the solvability of this problem is presented. Explicit expressions of a desired output feedback controller are proposed when the given LMIs are feasible. The effectiveness and the applicability of the proposed design approach are demonstrated by applying this to the problem of robust H∞ control for a class of uncertain nonlinear discrete delay systems.

This paper is concerned with the problem of robust H∞ filtering for linear systems with both discrete and distributed delays, which are subject to norm-bounded time-varying parameter uncertainties. Both the state and measurement equations are assumed to have discrete and distributed delays. A delay-dependent condition for the existence of H∞ filters is proposed, which is less conservative than existing ones in the literature. Via solutions to certain linear matrix inequalities, general full-order filters are designed that ensure asymptotic stability and a prescribed H∞ performance level, irrespective of the parameter uncertainties. An illustrative example is provided to demonstrate the effectiveness and the reduced conservatism of the proposed method.

This paper deals with the problem of H∞ output feedback control for uncertain stochastic systems with time-varying delays. The parameter uncertainties are assumed to be time-varying norm-bounded. The aim is the design of a full-order dynamic output feedback controller ensuring robust exponential mean-square stability and a prescribed H∞ performance level for the resulting closed-loop system, irrespective of the uncertainties. A sufficient condition for the existence of such an output feedback controller is obtained and the expression of desired controllers is given