Dwell time-based stabilisation of switched delay systems using free-weighting matrices


KORU A. T. , DELİBAŞI A. , Ozbay H.

INTERNATIONAL JOURNAL OF CONTROL, vol.91, no.1, pp.1-11, 2018 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 91 Issue: 1
  • Publication Date: 2018
  • Doi Number: 10.1080/00207179.2016.1266515
  • Title of Journal : INTERNATIONAL JOURNAL OF CONTROL
  • Page Numbers: pp.1-11

Abstract

In this paper, we present a quasi-convex optimisation method to minimise an upper bound of the dwell time for stability of switched delay systems. Piecewise Lyapunov-Krasovskii functionals are introduced and the upper bound for the derivative of Lyapunov functionals is estimated by free-weighting matrices method to investigate non-switching stability of each candidate subsystems. Then, a sufficient condition for the dwell time is derived to guarantee the asymptotic stability of the switched delay system. Once these conditions are represented by a set of linear matrix inequalities, dwell time optimisation problem can be formulated as a standard quasi-convex optimisation problem. Numerical examples are given to illustrate the improvements over previously obtained dwell time bounds. Using the results obtained in the stability case, we present a nonlinear minimisation algorithm to synthesise the dwell time minimiser controllers. The algorithm solves the problem with successive linearisation of nonlinear conditions.