<p>This article investigates switching control (SC) for the dissipative analysis of polynomial fuzzy systems (PFSs) with time-varying delays (TVDs) by introducing a novel membership-difference-dependent (MD-dependent) switching strategy. Unlike conventional switching mechanisms that rely solely on membership values or fixed rules, the proposed approach utilizes the difference between membership functions, enabling more sensitive and accurate detection of system variations. This leads to reduced conservatism, improved switching precision, and enhanced robustness under dynamic and uncertain conditions. The developed framework effectively captures the influence of TVDs, making it well-suited for real-world systems subject to unpredictable delays. To guarantee stability and dissipativity, a class of Lyapunov-Krasovskii functionals (LKFs) incorporating double integral terms is constructed, and tractable conditions are derived using a sum-of-squares (SOS) approach combined with parameter-dependent reciprocally convex inequalities. The proposed MD-based switching control not only improves system performance compared to traditional schemes but also ensures reliable operation in practical scenarios. Finally, the effectiveness and real-world applicability of the method are demonstrated through its implementation on an inverted pendulum system, highlighting its superiority in terms of stability and control performance.</p>

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Dissipative Analysis of Polynomial Fuzzy Systems with Time-Varying Delay via Membership-Difference-Dependent Switching Control

  • A. Chandrasekar,
  • T. Radhika,
  • Hijaz Ahmad,
  • Dilber Uzun Ozsahin,
  • Syed M. Hussain

摘要

This article investigates switching control (SC) for the dissipative analysis of polynomial fuzzy systems (PFSs) with time-varying delays (TVDs) by introducing a novel membership-difference-dependent (MD-dependent) switching strategy. Unlike conventional switching mechanisms that rely solely on membership values or fixed rules, the proposed approach utilizes the difference between membership functions, enabling more sensitive and accurate detection of system variations. This leads to reduced conservatism, improved switching precision, and enhanced robustness under dynamic and uncertain conditions. The developed framework effectively captures the influence of TVDs, making it well-suited for real-world systems subject to unpredictable delays. To guarantee stability and dissipativity, a class of Lyapunov-Krasovskii functionals (LKFs) incorporating double integral terms is constructed, and tractable conditions are derived using a sum-of-squares (SOS) approach combined with parameter-dependent reciprocally convex inequalities. The proposed MD-based switching control not only improves system performance compared to traditional schemes but also ensures reliable operation in practical scenarios. Finally, the effectiveness and real-world applicability of the method are demonstrated through its implementation on an inverted pendulum system, highlighting its superiority in terms of stability and control performance.