Modal and transition dwell time computation in switching systems: A set-theoretic approach

We consider a plant the dynamics of which switch among a family of systems. Each of these systems has a single stable equilibrium point. We assume that a constraint region for the state is assigned and we consider the problem of finding suitable limitations on the commutation speed in order to avoid constraints violations, even in the absence of state measurements. We introduce the concepts of modal and transition dwell times which lead to the definition of dwell time vector and dwell time graph (represented by a proper matrix), respectively. The former imposes a minimum permanence time on a discrete mode before commuting, the latter imposes the minimum permanence time on the current mode before switching to a specific new one. Both dwell time vector and dwell time graph can be computed via set-theoretic techniques. When the systems share a single equilibrium state, stability can be assured as a special case. Finally, under the assumption of affine dynamics, non-conservative values are achieved.