Slow State Variables Feedback Stabilization for Semi-Markov Jump Systems With Singular Perturbations

• Published in: IEEE transactions on automatic control Vol. 63; no. 8; pp. 2709 - 2714
• Main Authors: Shen, Hao, Li, Feng, Xu, Shengyuan, Sreeram, Victor
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Closed loop systems; Control systems design; Decoupling method; Discrete time systems; Feedback control; Integrated circuit modeling; Kernel; Markov chains; Markov processes; Parameters; Perturbation methods; Probability density function; Semi-Markov jump systems (SMJSs); semi-Markov kernel approach; Singular perturbation; singular perturbations; sojourn-time-dependent conditions; Stabilization; State variable; Symmetric matrices; Time dependence; Upper bound
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2017.2774006

The slow state variables feedback stabilization problem for semi-Markov jump discrete-time systems with slow sampling singular perturbations is discussed in this work. A new fairly comprehensive system model, semi-Markov jump system with singular perturbations, which is more general than Markov jump model, is employed to describe the phenomena of random abrupt changes in structure and parameters of the systems. Based on a slow state variables feedback control scheme, a novel technique to design the desired controller is presented and the allowed maximum of singular perturbation parameter can be calculated. With the help of the discrete-time semi-Markov kernel approach, some sojourn-time-dependent and less-conservative sufficient conditions are established via a novel matrix decoupling technique to ensure the solvability of the problem to be addressed. Finally, an illustrative example is given to show the superiority and usefulness of the proposed method.