Optimal Switching of Switched Systems with Time Delay in Discrete Time

Wei Xu, Zhi Guo Feng, Gui Hua Lin, Ka Fai Cedric Yiu, Liying Yu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

18 Citations (Scopus)


This paper addresses a kind of optimal switching problem to minimize a quadratic cost functional for the discrete-time switched linear system with time delay. Since the dynamics is influenced by the switching sequence and the time delay, most existing gradient-based methods and relaxation techniques cannot be applied. In order to find the optimal solution, we first formulate the switched time-delay system into an equivalent switched system to separate the cross term of coefficient matrices. Based on the positive semi-definiteness of the system, we derive a series of lower bounds of the cost functional. By comparing them with the current optimal value, a depth-first branch and bound technique is proposed and the global optimal solution can be exactly obtained. Some numerical examples are demonstrated to verify the high efficiency of the method.

Original languageEnglish
Article number108696
Publication statusPublished - Feb 2020


  • Branch and bound technique
  • Optimal switching problem
  • Switched systems
  • Time delay

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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