H₂ and H_∞ Performance Optimization of Singularly Perturbed Switched Systems

This paper addresses the H₂ and H_∞ performance problems for singularly perturbed switched linear systems in continuous time. We first propose a new and unified approach for stability analysis and norms computations for singularly perturbed linear time invariant systems. We generalize this approach to the case of singularly perturbed switched linear systems to obtain numerically well conditioned conditions for the design of a state-switching control. Such a switching strategy guarantees that the closed-loop switched system is globally asymptotically stable for sufficiently small values of the perturbation parameter and provides an upper bound to an H₂ and H_∞ performance index. We show that this approach can also be used for singularly perturbed switched linear systems with arbitrary switching rules and we provide a comparison with existing methods.