Average Dwell-Time Minimization of Switched Systems via Sequential Convex Programming

This work finds a lower bound on the average dwell-time (ADT) of switching signals such that a continuous-time, graph-based, switched system is globally asymptotically stable, input-to-state stable, or integral input-to-state stable. We first formulate the lower bound on the ADT as a nonconvex optimization problem with bilinear matrix inequality constraints. Because this formulation is independent of the choice of Lyapunov functions, its solution gives a less conservative lower bound than previous Lyapunov-function-based approaches. We then design a numerical iterative algorithm to solve the optimization based on sequential convex programming with a convex-concave decomposition of the constraints. We analyze the convergence properties of the proposed algorithm, establishing the monotonic evolution of the estimates of the average dwell-time lower bound. Finally, we demonstrate the benefits of the proposed approach in two examples and compare it against other baseline methods.