Finite-time control for discrete-time Markovian jump systems with deterministic switching and time-delay

• Published in: International journal of control, automation, and systems Vol. 12; no. 3; pp. 473 - 485
• Main Authors: Wen, Jiwei, Peng, Li, Nguang, Sing Kiong
• Format: Journal Article
• Language: English
• Published: Heidelberg Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.06.2014; Springer Nature B.V; 제어·로봇·시스템학회
• Subjects: Attenuation; Closed loop systems; Control; Control systems; Controllers; Disturbances; Engineering; Euclidean space; Gain; Government spending; Markov processes; Mechatronics; Process controls; Regular Papers; Robotics; Stochasticity; Studies; Switches; Switching; 제어계측공학; finite-time weighted; switching dynamics Markovian jump linear system; finite-time boundedness; Average dwell time; gain
• ISSN: 1598-6446; 2005-4092
• DOI: 10.1007/s12555-013-0397-x

In this paper, the finite-time control problem is investigated for a class of discrete-time Markovian jump systems (MJLSs) with deterministic switching and time-delay. The considered systems are subject to a piecewise-constant transition probability (TP) matrix, which leads to both the deterministic switches and stochastic jumps. First, the stochastic finite-time boundedness (SFTB) and l 2 gain analysis for the systems are studied by employing the average dwell time (ADT) approach. Note that a finite-time weighted l 2 gain is obtained to measure the disturbance attenuation level. Then, the mode-dependent and variation-dependent controller is designed such that the resulting closed-loop systems are stochastically finite-time bounded and have a guaranteed disturbance attenuation level. Finally, a numerical example is given to verify the potential of the developed results.