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Keywords:

  • time delay;
  • stabilization;
  • networked control systems;
  • linear matrix inequalities (LMIs)

SUMMARY

This paper is concerned with the stability and stabilization problems for a class of time-delayed systems, whose time-varying delays are studied via Markovian approach. By separating the delay interval into several subintervals and by considering the inherent distribution of time-varying delay, a new model is firstly developed. On the basis of the established model, a novel Lyapunov functional, which makes full use of each subinterval's delay bounds and the randomicity of time-varying delay, is constructed to drive less conservative stability criteria. Especially sufficient conditions for the existence of stabilizing controllers are obtained as linear matrix inequalities, which are further used to deal with networked control systems. Finally, numerical examples are used to demonstrate the effectiveness of the proposed methods. Copyright © 2012 John Wiley & Sons, Ltd.