Stochastic stability and optimal control for a class of continuous-time Markov jump linear systems with horizon defined by a stopping time

Abstract

This article deals with stochastic stability and optimal control for continuous-time Markov jump linear systems (MJLS). In the adopted model, the horizon of the problem is given by a stopping time representing the occurrence of a fix number N of failures or repair periods (T-N) after which the system is brought to a halt for maintenance. The stochastic stability in the appropriate sense is studied and a reconfigurable controller is derived at each jump time in the form of a linear feedback gain. The available information to the controller includes the imperfect knowledge of the jump state. In this framework, an optimal solution for the problem with complete Markov state observation, and a sub-optimal solution for the problem with incomplete state observation are presented. Both solutions are based on linear matrix inequalities (LMI).