Stabilization of semi-Markovian jump systems via a quantity limited controller

This paper addresses the stabilization problem of continuous-time semi-Markovian jump systems (s-MJSs), where the quantity of a controller to be designed has a limitation. A principle designing such a controller is proposed based on its stationary probability sequence. Sufficient conditions for the existence of the designed controller are obtained by applying a Lyapunov function approach and presented with LMIs. The controller mentioned above is proved to be a minimal variance approximation of mode-dependent controllers having total modes. More special cases about Markovian switching and without minimal variance approximation are further studied. A practical example is used to demonstrate the effectiveness and superiority of the proposed methods. (C) 2021 Elsevier Ltd. All rights reserved.