Admissibility analysis of discrete linear time-varying descriptor systems

This paper deals with the problem of admissibility analysis (i.e. regularity, causality and exponential stability) of discrete-time linear descriptor systems with uncertain time-varying parameters in the system state-space model matrices. The parameters enter affinely into all the matrices, and both their admissible values and variations are assumed to belong to given intervals. First, necessary and sufficient admissibility conditions for uncertainty-free discrete linear time-varying descriptor systems are presented. Next, strict linear matrix inequality conditions based on parameter-dependent Lyapunov functions are proposed to ensure robust admissibility of uncertain linear descriptor systems. Both the cases of Lyapunov functions with affine and quadratic dependence on the system uncertain parameters are considered. The robust admissibility analysis methods incorporate information on available bounds on both the admissible values and variation of the uncertain parameters. Numerical examples are presented to demonstrate the potentials of the proposed methods.