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

We consider a plant switching among a set of dynamic systems each associated with a single stable equilibrium point. We assume that a constraint region for the state is assigned. The main problem is that 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 a dwell time vector and dwell time graph (represented by a proper matrix), respectively. The former imposes a minimum permanence on a discrete mode before commuting, the second imposes the minimum permanence 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 systems share a single equilibrium stability can be assured as a special case. Finally, under the assumption of affine dynamics, non-conservative values are achieved.