Novel Practical Stability Conditions for Discrete-Time Switched Affine Systems

Abstract

This technical note proposes novel state feedback stability conditions based on the so called Lyapunov–Metzler inequalities for discrete-time switched affine systems, assuring practical stability of a desired equilibrium point. These conditions are obtained taking into account the volume minimization of an ellipsoidal set containing the nonconvex set of attraction to where the state trajectories are globally attracted. Compared with other recent results, the present ones are based on less conservative conditions for the existence of an attraction set. Moreover, it is not required that the equilibrium point be inside a predetermined set of attainable ones, which enlarges the range of applicability of the present technique. To the best of the authors’ knowledge, it is the first time that the Lyapunov–Metzler inequalities are adopted in the context of switched affine systems. As a second step, the associated nonconvex invariant set is provided. Academical examples illustrate the method and compare the theoretical results with recent ones available in the literature.