An adaptive sliding mode approach for Markovian jump systems with uncertain mode-dependent time-varying delays and partly unknown transition probabilities

  • Nasibeh Zohrabi
  • Hasan Zakeri
  • Amir Hossein Abolmasoumi
  • Hamid Reza Momeni
Article
  • 16 Downloads

Abstract

This paper deals with the problems of stochastic stability and sliding mode control for a class of continuous-time Markovian jump systems with mode-dependent time-varying delays and partly unknown transition probabilities. The design method is general enough to cover a wide spectrum of systems from those with completely known transition probability rates to those with completely unknown transition probability rates. Based on some mode-dependent Lyapunov–Krasovski functionals and making use of the free-connection weighting matrices, new delay-dependent conditions guaranteeing the existence of linear switching surfaces and the stochastic stability of sliding mode dynamics are derived in terms of linear matrix inequalities (LMIs). Then, a sliding mode controller is designed such that the resulted closed-loop system’s trajectories converge to predefined sliding surfaces in a finite time and remain there for all subsequent times. This paper also proposes an adaptive sliding mode controller design method which applies to cases in which mode-dependent time-varying delays are unknown. All the conditions obtained in this paper are in terms of LMI feasibility problems. Numerical examples are given to illustrate the effectiveness of the proposed methods.

Keywords

Linear matrix inequality (LMI) Markovian jump systems (MJSs) Mode-dependent time-varying delay Partly unknown transition probabilities Sliding mode control Stochastic stability 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringMississippi State UniversityMississippi StateUSA
  2. 2.Department of Electrical EngineeringUniversity of Notre DameNotre DameUSA
  3. 3.Department of Electrical EngineeringArak UniversityArakIran
  4. 4.Department of Electrical EngineeringTarbiat Modares UniversityTehranIran

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