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Improved higher-order Wirtinger integral inequality and switching mode design for nonlinear time-delay systems

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Listed:
  • Wang, Xiao-Yan
  • Long, Yue

Abstract

In this paper, the stability problem dependent on both the time delay and its derivative is analyzed for a class of nonlinear systems with time-varying delays using the T-S fuzzy approach. According to its derivative, is categorized as either monotonically increasing or decreasing, thus modeling it as a switched system. A high-order Wirtinger-type integral inequality is proposed. By introducing double and triple integral terms and combining the techniques of piecewise interval division and relaxation matrix decomposition, the tightness of the lower-bound estimation is improved. Furthermore, a novel mode-dependent Lyapunov-Krasovskii functional is designed, where the matrix terms are time-varying and allow different Lyapunov matrices for different delay variation modes. By using the average dwell time method, a condition for exponential stability of the fuzzy system is derived. Finally, the effectiveness and advantages of the proposed method are verified through a simulation example of a liquid monopropellant rocket engine model.

Suggested Citation

  • Wang, Xiao-Yan & Long, Yue, 2026. "Improved higher-order Wirtinger integral inequality and switching mode design for nonlinear time-delay systems," Applied Mathematics and Computation, Elsevier, vol. 522(C).
    • Handle: RePEc:eee:apmaco:v:522:y:2026:i:c:s0096300326000494
    DOI: 10.1016/j.amc.2026.129997
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