Constraint satisfaction for switched linear systems with restricted dwell-time

This paper considers the control of constrained linear systems with dynamics and constraints that change as a function of time according to an unknown exogenous switching signal that satisfies dwell-time restrictions. We characterize the set of initial conditions for which it is possible to guarantee constraint satisfaction for any admissible switching signal. We define the concept of control (positive) switch-invariant sets which are control (positive) invariant sets with the additional property that it is possible to transition between the control (positive) switch-invariant sets without violating constraints. It is possible to guarantee constraint satisfaction for a given initial condition if the control (positive) switch-invariant set of a mode can be reached from it within the dwell-time of that mode. An algorithm is presented for computing the maximal control (positive) switch-invariant sets. Finally, we demonstrate the theory developed in this paper on a vehicle lane changing case study.