Finite-time analysis and design for discrete-time switching dynamics Markovian jump linear systems with time-varying delay

• Published in: IET control theory & applications Vol. 8; no. 17; pp. 1972 - 1985
• Main Authors: Wen, Jiwei, Peng, Li, Nguang, Sing Kiong
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 20.11.2014
• Subjects: ADT switching; Delay; delays; Design analysis; Design engineering; discrete‐time switching dynamics Markovian jump linear systems; disturbance attenuation capability; Dynamical systems; Dynamics; finite‐time analysis; fixed time interval; high‐level average dwell time switching; Linear systems; Markov processes; matrix algebra; piecewise‐constant transition probability matrix; SD‐MJLS; stochastic finite‐time boundedness; stochastic systems; sufficient conditions; Switching; time‐varying delay; time-varying delay; high-level average dwell time switching; finite-time analysis; ADT switching; discrete-time switching dynamics Markovian jump linear systems; piecewise-constant transition probability matrix; linear systems; SD-MJLS; matrix algebra; disturbance attenuation capability; sufficient conditions; delays; Markov processes; stochastic systems; stochastic finite-time boundedness; fixed time interval
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/iet-cta.2014.0622

The problems of finite-time analysis and design for a class of discrete-time switching dynamics Markovian jump linear systems (SD-MJLSs) with time-varying delay are investigated in this study. The considered systems could be viewed as Markovian jump linear systems governed by a piecewise-constant transition probability matrix, which is subject to a high-level average dwell time (ADT) switching. The time delay is considered as time varying and has a lower and upper bound. First, sufficient conditions, which guarantee the stochastic finite-time boundedness of the underlying systems, are presented by employing the ADT approach. These conditions are not only dependent on the delay upper bound but also the delay range. Then, a finite-time weighted l2 gain of such delay SD-MJLSs is obtained to measure the disturbance attenuation capability over a fixed time interval and the design of the stabilising controller is further given. Moreover, an improved controller design method, which could provide efficiency and practicability, is further developed. Finally, a numerical example is given to verify the potential of the developed results.