Further enhancement on H∞ sliding mode control design for singular Markovian jump systems with partly known transition probabilities

Fallah Z., Baradarannia M., Kharrati H., Hashemzadeh F.

JVC/Journal of Vibration and Control, vol.28, no.9-10, pp.1187-1199, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 9-10
  • Publication Date: 2022
  • Doi Number: 10.1177/1077546321989202
  • Journal Name: JVC/Journal of Vibration and Control
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Compendex, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.1187-1199
  • Keywords: H∞ control, Markovian jump systems, singular systems, sliding mode control, stochastic control
  • Istanbul Technical University Affiliated: No


This study considers the designing of the H∞ sliding mode controller for a singular Markovian jump system described by discrete-time state-space realization. The system under investigation is subject to both matched and mismatched external disturbances, and the transition probability matrix of the underlying Markov chain is considered to be partly available. A new sufficient condition is developed in terms of linear matrix inequalities to determine the mode-dependent parameter of the proposed quasi-sliding surface such that the stochastic admissibility with a prescribed H∞ performance of the sliding mode dynamics is guaranteed. Furthermore, the sliding mode controller is designed to assure that the state trajectories of the system will be driven onto the quasi-sliding surface and remain in there afterward. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design algorithms.