Robust exponential stabilization of a certain class of switched systems

In this paper we consider continuous-time switched systems whose subsystems are linear, or, more generally, homogeneous of degree one. For that class of systems, we present a control algorithm that under certain conditions generates switching signals that globally exponentially stabilizes the switched system, even in the case in which there are model uncertainties and/or measurement errors, provided that the bounds of that uncertainties and errors depend linearly on the norm of the state of the system and are small enough in a suitable sense. We also show that in the case in which the measurement errors and the model uncertainties are bounded, the algorithm globally exponentially stabilizes the system in a practical sense, with a final error which depends linearly on the bounds of both the model uncertainties and the measurement errors. Finally, we illustrate the behaviour of the algorithm by means of simulations.