Dwell-time approach to input-output stability properties for discrete-time linear hybrid systems

Motivated by studying a sampled-data (or discrete-time) version of switched linear systems, we consider a class of time-varying dynamical systems that consist of switching of a number of discrete-time linear time-invariant (sub)systems. For these systems, we propose LMI (Linear Matrix Inequality) formulations of analyzing their input-output stability properties, including both ℓ-2 stability and passivity, by constraining switching signals via the concept of dwell time. As a natural byproduct, we provide a numerical procedure of optimally computing ℓ-2 bounds with respect to dwell time for switched linear systems in the discrete-time setting. Finally, the LMI formulation of ℓ-2 stability is applied to evaluating control system performance for an industrial refrigeration process that is regulated by several switched proportional-integral (PI) controllers.