A new condition for asymptotic stability of uncertain discrete-time systems: it is less conservative than the quadratic stability condition

We consider a linear discrete-time system depending multi-affinely on a vector of uncertain time-varying parameters. A condition guaranteeing asymptotic stability of such a system is the classical quadratic stability test. In Amato et al. (1998), a necessary and sufficient condition for quadratic stability has been provided in terms of a feasibility problem involving linear matrix inequalities. We provide a condition for asymptotic stability of the class of systems under consideration which is less conservative than the quadratic stability condition. A numerical example illustrates the proposed technique