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...

In the sequel to [12], we discuss behavioural approach for linear, time-varying, differential algebraic (descriptor) systems with real analytic coefficients. The analysis is “almost global” in the sense that the analysis is not restricted to an interval I ⊂ R but is allowed for the “time axis” R\T, where T is a discrete set of critical points, at which the solution may exhibit a finite escape t...

In this paper we consider models for noncausal processes consisting of discrete-time descriptor dynamics and boundary conditions on the values of the process at the two ends of the interval on which the process is defined. We discuss the general solution and well-posedness of systems of this type and then apply the method of complementary processes to obtain a specification of the optimal smoot...

This paper presents a new and less conservative condition for the robust stability test of discrete-time polytopic systems by using a descriptor system approach. The stability condition is formulated in terms of a set of linear matrix inequalities and can be easily adapted for robust controller synthesis. The developed results can be viewed as a discretetime counterpart of the continuous-time o...