LMI-based stability tests for LPV and switched discrete-time linear systems through redundant equations^⁎

This paper revisits the problem of testing the robust stability of discrete-time linear systems with arbitrarily fast time-varying parameters, which includes the important class of switched discrete-time linear systems with arbitrary switching. By exploring the redundant description of the state space equations, sufficient linear matrix inequality (LMI) conditions of distinct complexities assuring robust stability are given in terms of the number k—1 of redundant equations. As k ≥ 1 increases, the conditions become also asymptotically necessary. Numerical examples borrowed from the literature illustrate that the proposed conditions can be computationally less demanding than other convergent relaxations.