Robust stability of discrete-time linear descriptor systems with time-varying uncertainties via parametric Lyapunov function

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. The parameters enter affinely into the state matrix of the system state-space model, and 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 LMI conditions based on parameter-dependent Lyapunov functions are proposed to ensure robust admissibility of uncertain 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.