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Stabilization of Switched Linear Systems Using Continuous Control Input against Known Adversarial Switching

The problem of designing continuous control input to stabilize switched linear control systems against adversarial switching is studied. It is assumed that the continuous controller has access to the current switching mode and can be of the form of an ensemble of mode-dependent state feedback controllers. The fastest stabilizing rate under the given information structure is proposed as a quantitative metric of the system’s stabilizability, and its bounds are derived using seminorms. Computation algorithms for the stabilizing rate are developed and illustrated through examples.