Robust uniformly ultimate boundedness control for uncertain switched linear systems

In this paper, piecewise linear switched systems affected by both parameter variations and exterior disturbances are considered. The problem of synthesis of switching laws, which assure that the system state is ultimately bounded within a given compact set containing the origin with an assigned rate of convergence, is investigated. Given an uncertain switched linear system, we present a systematic methodology for computing switching laws that guarantee ultimate boundedness. The method is based on set-induced Lyapunov functions. For systems with linearly constrained uncertainties, it is shown that such a function may be derived by numerically efficient algorithms involving polyhedral sets. Based on these Lyapunov functions, we compose global Lyapunov functions that guarantee ultimate boundedness for the switched linear system. The switching laws are characterized by computing conic partitions of the state space.