DOI: 10.1049/cth2.12632 ISSN: 1751-8644

Stability analysis of discrete‐time systems with a time‐varying delay via improved methods

Hongjia Sha, Ju H. Park, Jun Chen, Mingbo Zhu, Chengjie Nan
  • Electrical and Electronic Engineering
  • Control and Optimization
  • Computer Science Applications
  • Human-Computer Interaction
  • Control and Systems Engineering


This paper is concerned with the stability analysis of discrete‐time systems with a time‐varying delay. The conservatism and computation burden are two important factors to evaluate a stability condition. By taking the relationship of two reciprocally convex parts into consideration, a new combined matrix‐separation‐based inequality is proposed that involves only a few free matrices. Moreover, an improved matrix‐injection‐based transformation lemma with the parameter varying within a closed interval is proposed by introducing only one free matrix. By constructing an appropriate Lyapunov–Krasovskii functional and applying the improved methods, a relaxed stability condition is consequently obtained with a small number of decision variables. Two numerical examples are given to show the merits of the proposed methods.

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