Mixed control of delayed Markov jump linear systems

Abstract

This study investigates the state feedback control laws for Markov jump linear systems with state and mode‐observation delays. An assumption in this study is that the delay of the mode observation obeys an exponential distribution. Also, the authors raise an unknown time‐varying state delay applied in the composition of the state feedback controller. A method of remodelling the closed‐loop system as a standard Markov jump linear system with state delay is shown. Furthermore, on the basis of this remodelling, several linear matrix inequalities for designing feedback gains for stabilisation and mixed control are proposed. Finally, the authors apply a numerical simulation for examining the effectiveness of the proposed mixed controller designing method.