Delay-distribution-dependent robust stability of uncertain systems with time-varying delay

Authors

  • Dong Yue,

    Corresponding author
    1. Institute of Information and Control Engineering, Nanjing Normal University, Nanjing, People's Republic of China
    • Institute of Information and Control Engineering, Nanjing Normal University, 78 Bancang Street, 210042, Nanjing, People's Republic of China
    Search for more papers by this author
  • Engang Tian,

    1. Institute of Information and Control Engineering, Nanjing Normal University, Nanjing, People's Republic of China
    2. College of Information Sciences and Technology, Donghua University, Shanghai, People's Republic of China
    Search for more papers by this author
  • Yijun Zhang,

    1. Institute of Information and Control Engineering, Nanjing Normal University, Nanjing, People's Republic of China
    2. College of Information Sciences and Technology, Donghua University, Shanghai, People's Republic of China
    Search for more papers by this author
  • Chen Peng

    1. Institute of Information and Control Engineering, Nanjing Normal University, Nanjing, People's Republic of China
    Search for more papers by this author

Abstract

By employing the information of the probability distribution of the time delay, this paper investigates the problem of robust stability for uncertain systems with time-varying delay satisfying some probabilistic properties. Different from the common assumptions on the time delay in the existing literatures, it is assumed in this paper that the delay is random and its probability distribution is known a priori. In terms of the probability distribution of the delay, a new type of system model with stochastic parameter matrices is proposed. Based on the new system model, sufficient conditions for the exponential mean square stability of the original system are derived by using the Lyapunov functional method and the linear matrix inequality (LMI) technique. The derived criteria, which are expressed in terms of a set of LMIs, are delay-distribution-dependent, that is, the solvability of the criteria depends on not only the variation range of the delay but also the probability distribution of it. Finally, three numerical examples are given to illustrate the feasibility and effectiveness of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.

Ancillary