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access icon free Robust stabilisation for non-linear time-delay semi-Markovian jump systems via sliding mode control

  • Author(s): Wenhai Qi 1 ; Ju H. Park 2 ; Jun Cheng 3 ; Yonggui Kao 4
    • View affiliations
    • Affiliations: 1: Department of Automation, Qufu Normal University, Rizhao 276826, People's Republic of China ;
      2: Department of Electrical Engineering, Yeungnam University, 280 Daehak-Ro, Kyongsan 38541, Republic of Korea ;
      3: School of Science, Hubei University for Nationalities, Enshi 445000, People's Republic of China ;
      4: School of Science, Harbin Institute of Technology, Weihai 264209, People's Republic of China
  • Source: Volume 11, Issue 10, 23 June 2017, p. 1504 – 1513
    DOI:  10.1049/iet-cta.2016.1465 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 25/11/2016, Accepted 11/03/2017, Revised 05/02/2017, Published 15/03/2017

This study deals with the problem of robust stabilisation for non-linear time-delay semi-Markovian jump systems via sliding mode control (SMC). Such a switching is governed by a semi-Markovian process which is time-varying and dependent on the sojourn-time h. The time delay is considered as time-varying and meets the requirements of the upper and lower bounds. By introducing free-connection weighting matrix method and Lyapunov functional, sufficient conditions for the resulting sliding mode dynamics in the form of linear matrix inequalities are derived to guarantee the closed-loop system robustly stochastically stable for all admissible uncertainties and non-linear perturbations. Then, an SMC law is synthesised to drive the system trajectories onto the predefined switching surface in a finite time. Finally, an example illustrates the validity of the obtained results.

Inspec keywords: nonlinear systems; closed loop systems; stochastic systems; control system synthesis; variable structure systems; perturbation techniques; robust control; linear matrix inequalities; delays; uncertain systems

Other keywords: nonlinear perturbations; nonlinear time-delay semiMarkovian jump systems; sojourn-time; time-varying time delay; Lyapunov functional; sliding mode control; SMC law synthesis; free-connection weighting matrix method; system trajectories; SMC; switching surface; closed-loop system; admissible uncertainties; sliding mode dynamics; robust stabilisation; linear matrix inequalities

Subjects: Control system analysis and synthesis methods; Stability in control theory; Time-varying control systems; Algebra; Nonlinear control systems; Multivariable control systems; Distributed parameter control systems

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