EXPONENTIAL STABILITY OF UNCERTAIN SWITCHED LINEAR SYSTEMS

In this paper, sufficient conditions are proposed to investigate the robust stability of arbitrary switched linear systems with uncertain parameters belongs to the known intervals. In addition, a method is then established to determine the maximum intervals of parameters' variations which guarantee robust exponential stability of uncertain switched linear systems under arbitrary switching. In the proposed method, the known information about the parametric structure of uncertainties is considered; therefore it will result in less conservative stability margins. A generalization of the method is also provided to determine stability bounds on perturbations of entries in subsystem matrices, when subsystems are subjected to independent perturbations. Numerical examples are included to illustrate the effectiveness of the results, and compare them with the previous results. It is shown that the proposed methods provide stability intervals on the uncertain parameter for all switched linear systems which admit a common quadratic Lyapunov function for the nominal system.