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Keywords:

  • Markovian jump systems;
  • delay-range-dependent;
  • nonlinear disturbances;
  • mode-dependent time delays

Abstract

This paper discusses the robust stabilization problem for a class of Markovian jump systems with nonlinear disturbances and time delays, which are time-varying in intervals and depend on system mode. By exploiting a new Lyapunov–Krasovskii functional, which takes into account the range of delay and by making use of novel techniques, mean-square exponential stability result is proposed. Based on the obtained stability condition, a sufficient condition for state feedback controller, which stabilizes system and maximizes the bound on nonlinear perturbations is derived in terms of linear matrix inequalities involving a convex optimization. Finally, illustrative examples are presented to show the benefits and effectiveness of the proposed approaches. Copyright © 2009 John Wiley & Sons, Ltd.