Characterizing uniformly ultimately bounded switching signals for uncertain switched linear systems

In this paper, the uniformly ultimately bounded (UUB) switching control problem is investigated for a class of continuous-time switched linear systems with parametric uncertainties and exterior disturbances. It is assumed that each subsystem is UUB. First, a class of switching signals, which may contains infinite number of switching and preserves the UUB of the switched systems, is characterized. Then, a switching law is synthesized to improve the disturbance attenuation properties in the sense that all state trajectories can converge into a smaller region than any single subsystem acts alone. The switching law is given as a static state feedback form, and provides a conic partition of the state space. To avoid unstable sliding motions, some modifications are introduced later. The techniques are based on multiple polyhedral Lyapunov functions.