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Optimization of average dwell-time lower bound for switched systems via sequential convex programming
S. Liu, S. Martínez, J. Cortés
IEEE Control Systems Letters 6 (2022), 1076-1081

Abstract

This work finds a non-conservative lower bound on the average dwell-time 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. Unlike previous lower bounds proposed in the literature, which depend on the choice of Lyapunov functions and hence may be conservative, we optimize the average dwell-time lower bound by means of a nonconvex optimization problem with bilinear matrix inequality constraints. We then design a numerical iterative algorithm based on sequential convex programming to solve the optimization. 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 present two examples to demonstrate the benefits of the proposed approach and compare it against other baseline methods.

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