In this article a detailed overview of Lyapunov stability of linear continuous systems is presented. The conditions for the existence of the solutions for both regular and irregular singular linear systems are introduced. To guarantee an asymptotical stability for linear continuous singular systems and to provide an impulse-free motion of the system, new stability conditions are analyzed. In th...

This paper concerns the problem of output strictly passive control for uncertain singular neutral systems. It introduces a new effective criterion to study the passivity of singular neutral systems. Compared with the previous approach, this criterion has no equality constraints. And the state feedback controller is designed so that the uncertain singular neutral systems are output strictly pass...

The geometric approach is a mathematical concept developed to improve the analysis and synthesis of linear multivariable systems. In this article we summarized the foundations for the geometric approach to both linear and singular systems. A mathematical introduction to the controlled and conditioned invariant subspaces has been presented. Additional characteristic subspaces were introduced, su...

The stability and stabilization of linear continuous time singular Markov switched systems with time delay are investigated. Based on the linear matrix inequality method (LMIs), the robust stability of uncertain linear stochastic delay system is guaranteed irrespective of the value of the time delay. Then the proposed theory can be extended to discuss the robust stabilization of uncertain stoch...

Descriptor systems which are also referred to as singular systems are described by differential equations and algebraic equations [1]. It has been widely applied in the areas of power systems, economic systems, biological systems, constrained robots, electronic networking, aerospace, chemical process and astronomy (solar activity)[1-4]. Stability of descriptor systems is a basic and important p...

Abstract In this paper, we propose a new method to design an observer for a class of non linear singular systems described by Takagi-Sugeno (TS) model, with measurable decision variables. The idea of the proposed approach is based on the singular value decomposition. The convergence of the state estimation error is studied using the Lyapunov theory and the stability conditions are given in term...

This paper discusses robust stochastic stability and stabilization of time-delay discrete Markovian jump singular systems with parameter uncertainties. Based on the restricted system equivalent (RES) transformation, a delay-dependent linear matrix inequalities condition for time-delay discrete-time Markovian jump singular systems to be regular, causal and stochastically stable is established. W...

The index of matrix A in Cn.n is equivalent to the dimension of largest Jor-dan block corresponding to the zero eigenvalue of A. In this paper, indicialequations and normal equations for solving inconsistent singular linear systemof equations are investigated.