We establish a unified approach to stability analysis for switched linear descriptor systems under arbitrary switching in both continuous-time and discrete-time domains. The approach is based on common quadratic Lyapunov functions incorporated with linear matrix inequalities (LMIs). We show that if there is a common quadratic Lyapunov function for the stability of all subsystems, then the switc...

In this paper necessary and sufficient conditions are derived for complete reachability and observability of periodic time-varying descriptor systems. Applying these conditions, the symmetric positive semi-definite reachability/observability Gramians are defined and can be shown to satisfy some projected generalized discrete-time periodic Lyapunov equations. We propose a numerical method for so...

This paper deals with discrete-time stochastic descriptor (singular) systems with instantaneous and multi-time delayed measurements. The estimability condition of the descriptor systems involving delayed measurements is given. Using the measurements reorganization approach, the optimal Kalman …lter and corresponding estimate error covariance are derived. Furthermore, an algorithm for the linear...

Descriptor (singular) linear systems have been considered in many papers and books (Bru et al., 2003; 2002; Choundhury, 1972; Campbell et al., 1976; Dai, 1989; Guang-Ren Duan, 2010; Kaczorek, 2013; 2011a; 2014b; 2004; 1992; 2014c; 2011c; 2011d; 2011e; Virnik, 2008). The eigenvalue and invariant assignment by state and output feedbacks was investigated by Kaczorek (2004; 2011d), along with minim...

This paper is concerned with the problem of robust filtering for uncertain linear discrete-time descriptor systems. The matrices of the system state-space model are uncertain and supposed to belong to a given polytope. A linear matrix inequality based method is proposed for designing linear stationary strictly proper filters that guarantee the asymptotic stability of the estimation error and an...

A method of analysis of descriptor nonlinear discrete-time systems with regular pencils of linear part is proposed. The method is based on the Weierstrass-Kronecker decomposition of the pencils. Necessary and sufficient conditions for the positivity of the nonlinear systems are established. A procedure for computing the solution to the equations describing the nonlinear systems are proposed and...

From the necessary and sufficient conditions for complete reachability and observability of periodic time-varying descriptor systems, the symmetric positive semi-definite reachability/observability Gramians are defined. These Gramians can be shown to satisfy some projected generalized discrete-time periodic Lyapunov equations. We propose a numerical method for solving these projected Lyapunov e...

This paper considers actuator-fault estimation for discrete-time descriptor systems with unknown but bounded system disturbance and measurement noise. A zonotopic fault estimation filter is designed based on the analysis of fault detectability indexes. To ensure estimation accuracy, the filter gain in the zonotopic fault estimation filter is optimized through the zonotope minimization. The desi...

We investigate the robust stabilization problem for the descriptor discrete-time systems and build an optimal solution in the case when both the nominal system and the perturbations are given in terms of left coprime factorizations over RH∞. Numerically reliable solutions are given for both the stability radius and the associated controller, which, in addition, regain the same simplicity as in ...

This paper deals with the H∞ recursive estimation problem for general rectangular time-variant descriptor systems in discrete time. Riccati-equation based recursions for filtered and predicted estimates are developed based on a data fitting approach and game theory. In this approach, the nature determines a state sequence seeking to maximize the estimation cost, whereas the estimator tries to f...