This note deals with the problems of robust stability and stabilization for uncertain discrete-time singular systems. The parameter uncertainties are assumed to be time-invariant and norm-bounded appearing in both the state and input matrices. A new necessary and sufficient condition for a discrete-time singular system to be regular, causal and stable is proposed in terms of a strict linear matrix inequality (LMI). Based on this, the concepts of generalized quadratic stability and generalized quadratic stabilization for uncertain discrete-time singular systems are introduced. Necessary and sufficient conditions for generalized quadratic stability and generalized quadratic stabilization are obtained in terms of a strict LMI and a set of matrix inequalities, respectively.With these conditions, the problems of robust stability and robust stabilization are solved. An explicit expression of a desired state feedback controller is also given, which involves no matrix decomposition. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.

This Letter investigates the problem of robust global exponential stability analysis for interval recurrent neural networks (RNNs) via the linear matrix inequality (LMI) approach. The values of the time-invariant uncertain parameters are assumed to be bounded within given compact sets. An improved condition for the existence of a unique equilibrium point and its global exponential stability of RNNs with known parameters is proposed. Based on this, a sufficient condition for the global robust exponential stability for interval RNNs is obtained. Both of the conditions are expressed in terms of LMIs, which can be checked easily by various recently developed convex optimization algorithms. Examples are provided to demonstrate the reduced conservatism of the proposed exponential stability condition.

This paper deals with the problems of positive real (PR) analysis and PR control for uncertain discrete-time descriptor systems. The parameter uncertainties are assumed to be time-invariant norm bounded and appear in both the state and input matrices. A new necessary and sufficient condition for a discrete-time descriptor system to be regular, causal, stable and extended strictly PR (ESPR) is proposed in terms of a strict linear matrix inequality. Based on this, the concepts of strong robust admissibility with ESPR and strong robust admissibilizability with ESPR were introduced. Without any additional assumptions on the system matrices, necessary and sufficient conditions for strong robust admissibility with ESPR and strong robust admissibilizability with ESPR are obtained. Through these results, the problems of PR analysis and PR control are solved. Furthermore, an explicit expression of a desired state feedback controller is also given, which involves no decomposition of the system matrices.

This note considers the problem of robust H∞ filtering for uncertain Markovian jump linear systems with time-delays which are timevarying and depend on the system mode. The parameter uncertainties are time-varying norm-bounded. The aim of this problem is to design a Markovian jump linear filter that ensures robust exponential mean-square stability of the filtering error system and a prescribed L2-induced gain from the noise signals to the estimation error, for all admissible uncertainties. A sufficient condition for the solvability of this problem is obtained. The desired filter can be constructed by solving a set of linear matrix inequalities. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach.

This note considers the H∞ filtering problem for linear continuous singular systems. The purpose is the design of a linear filter such that the resulting error system is regular, impulse-free and stable while the closed-loop transfer function from the disturbance to the filtering error output satisfies a prescribed H∞-norm bound constraint.Without decomposing the original system matrices, a necessary and sufficient condition for the solvability of this problem is obtained in terms of a set of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired filter is given. Finally, an illustrative example is presented to demonstrate the applicability of the proposed approach.