Dwell-time approach to input–output stability properties for a class of discrete-time dynamical systems

We consider a class of discrete-time dynamical systems that consist of switching of many linear time-invariant systems, and it can be used to cover a sampled-data version of Switched Linear Systems, which have been widely studied in the literature. For this class of dynamical systems, we establish the LMI (Linear Matrix Inequality) formulation of analyzing their input–output stability properties, including both ℓℓ-2 stability and passivity, by constraining switching signals via the concept of dwell time. The LMI formulation of ℓℓ-2 stability is applied to evaluating the closed-loop performance of an industrial refrigeration process that is regulated by several proportional-integral (PI) controllers in a switching structure.