Stabilisation of discrete-time switched nonlinear systems

The stabilisation problem for discrete-time switched nonlinear systems is studied under two different scenarios: time-dependent switching (open-loop control) and state-dependent switching (closed-loop control). In the first, global asymptotic stability of the zero equilibrium and a guaranteed performance are ensured by a switching rule subject to a persistent dwell time condition. In the second, a state-dependent switching function is designed to accomplish the same goals of stability and performance by means of conditions expressed in terms of a nonlinear version of the well-known Lyapunov-Metzler inequalities. A numerical method that applies to a subclass of nonlinear systems is proposed. It is able to check locally the sufficient conditions through the solution of a convex programming problem expressed by LMIs. Academic examples illustrate the theoretical results.