Synthesis of uniformly ultimate boundedness switching laws for discrete-time uncertain switched linear systems

In this paper, discrete-time switched linear systems affected by both parameter variations and exterior disturbances are considered. The problem of synthesis of switching control 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. The method is based on set-induced Lyapunov functions. Based on these Lyapunov functions, we compose a global Lyapunov function which guarantees ultimate boundedness for the switched system. The switching laws are characterized by computing conic partitions of the state space.