Bounded real lemma for discrete linear time-varying descriptor systems

This paper addresses the problem of admissibility analysis with a guaranteed bound on the system H
_∞
norm for discrete linear time-varying descriptor systems. Two equivalent necessary and sufficient versions of the bounded real lemma are derived based on strict matrix inequality constraints. Then, these results are applied to deal with uncertain descriptor systems in which all the system state-space matrices depend affinely on convex bounded uncertain time-varying parameters. Both affine and quadratic parameter-dependent Lyapunov functions are considered to evaluate robust H
_∞
performance in terms of linear matrix inequalities which incorporate available information on the variation of the uncertain parameters. A numerical example is presented to illustrate the approach.