Hidden Markov model based control for singular Markov jump systems

A hidden Markov model based control strategy is proposed to ensure the exponential mean-square admissible (EMS-admissible) of singular Markov jump systems (SMJSs) with mode-dependent singular matrix in this paper. The discontinuities caused by the mode-dependent singular matrix and Markov jump switching are investigated to make the results more practical. Concrete controller designing process is presented to tackle the instabilities brought by the hidden Markov model and the discontinuities. A new kind of Lyapunov function is constructed to characterize the switching features presented by Markov jump system and hidden Markov model based controller, which derives the stability conditions of the SMJSs. Then, a linearization strategy is proposed to reduce the coupled terms generated by the hidden Markov model. The hidden Markov model based controller is further designed based on the established conditions to ensure the EMS-admissible of the considered SMJSs. A numerical example and a direct current (DC) motor example are given to illustrate the effectiveness of the control approach. (C) 2021 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.