Stabilization of continuous-time Markovian jump systems: A mode separation but optimization method

Abstract

This paper addresses the stabilization problem of continuous-time Markovian jump systems (MJSs) by applying an optimization controller. A new stabilizing method based on a mode separation algorithm is proposed, whose separation will be optimized by minimizing the established cost function value. It will be seen that the presented optimal controller will have hybrid decision variables such as continuous and discrete variables. Meanwhile, the related cost function is in contrast to the traditionally linear quadratic functions. The conditions for the existence of the developed controller are established via using rigorous theory analysis, and its detailed computation method is presented too. It can be concluded that traditionally mode-dependent and -independent controllers about MJSs are contained as two special situations. A practical example is offered so as to verify the effectiveness and superiority of the methods proposed in this study.