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<p>This paper presents sufficient delay-dependent conditions for stability analysis and stabilization of nonlinear time-varying delay systems represented by a Takagi-Sugeno (TS) model. These conditions are reached by employing a non-quadratic Lyapunov-Krasovskii functional (NQLKF), considering a double integral term. The structure of the proposed NQLKF avoids the problem of handling the time derivatives of the membership functions that appear when fuzzy terms are considered in the functional. Also, two different integral inequalities are used to estimate the time derivative of the proposed NQLKF. Then, more relaxed conditions for stability and stabilization in terms of linear matrix inequalities (LMIs) are established. Some examples illustrate the proposed approaches’ effectiveness and applicability over previous results.</p>

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Reducing Conservativeness of LMI-based Stability and Stabilization Conditions for Nonlinear Time-varying Delay Systems Represented by Exact Takagi-Sugeno Models

  • 期刊论文

  • 发表日期：

    2025年4月12日

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  • Sara Angulo,
  • Raymundo Márquez,
  • Miguel Bernal

摘要

This paper presents sufficient delay-dependent conditions for stability analysis and stabilization of nonlinear time-varying delay systems represented by a Takagi-Sugeno (TS) model. These conditions are reached by employing a non-quadratic Lyapunov-Krasovskii functional (NQLKF), considering a double integral term. The structure of the proposed NQLKF avoids the problem of handling the time derivatives of the membership functions that appear when fuzzy terms are considered in the functional. Also, two different integral inequalities are used to estimate the time derivative of the proposed NQLKF. Then, more relaxed conditions for stability and stabilization in terms of linear matrix inequalities (LMIs) are established. Some examples illustrate the proposed approaches’ effectiveness and applicability over previous results.