ℋ2 Performance Optimization of Singularly Perturbed Switched Linear Systems

This paper addresses the ℋ2 performance problem for singularly perturbed switched linear systems in continuous-time. We propose a new and unified approach for stability analysis and norm computation for singularly perturbed LTI systems and generalize it 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 performance index. We provide a comparison with existing methods.