Stability and Stabilization for Singular Switching Semi-Markovian Jump Systems With Generally Uncertain Transition Rates

• Published in: IEEE transactions on automatic control Vol. 63; no. 11; pp. 3919 - 3926
• Main Authors: Jiang, Baoping, Kao, Yonggui, Karimi, Hamid Reza, Gao, Cunchen
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.11.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Controllers; Economic models; Feedback control; Linear matrix inequalities; Linear matrix inequalities (LMIs); Markov analysis; Markov processes; Mathematical analysis; Matrix methods; Numerical stability; semi-Markovian jump systems (S-MJS); singular systems; Stability; Stability criteria; Stabilization; State feedback; stochastic stability; Switches; Switching; Switching systems; Symmetric matrices
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2018.2819654

This paper studies the problems of stability and stabilization for a class of singular switching semi-Markovian jump systems. The general transition rates in the semi-Markov process cover completely unknown and uncertain bounded as two special cases. First, sufficient conditions are developed to ensure the unforced system to be regular, impulse-free, and exponentially mean-square stable. Then, by proposing a state feedback controller, sufficient conditions in terms of strict linear matrix inequalities are derived to guarantee the closed-loop system to be stochastically stabilziable. Finally, a numerical example is provided to show the effectiveness of the obtained results.