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<p>This paper addresses the output-feedback fault-tolerant control problem for uncertain time-delay systems subject to lumped external disturbances, parametric uncertainties, and actuator failures, where full state measurements are unavailable. An output-feedback disturbance observer (DOB) is developed to estimate the lumped disturbance in real time, and a disturbance-compensation-based control law is constructed to enhance robustness without additional state sensors. By employing a Lyapunov–Krasovskii functional, delay-dependent sufficient conditions for asymptotic stability are derived in terms of linear matrix inequalities (LMIs). To enable controller synthesis, Finsler’s lemma is utilized to decouple bilinear terms, resulting in a tractable convex framework for the simultaneous computation of the observer and controller gains. Comparative simulations against PID control, sliding mode control, and active disturbance rejection control demonstrate faster convergence, smaller overshoot, and improved disturbance attenuation of the proposed method. Hardware experiments on a rotary double inverted pendulum platform further validate the effectiveness and practical applicability of the proposed approach under input time delays and actuator degradation.</p>

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Control of Uncertain Double Inverted Pendulum System with Time Delay Based on Disturbance Observer

  • 期刊论文

  • 发表日期：

    2026年4月25日

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  • Laixin Gao,
  • Guangming Zhang,
  • Lingchun Li

摘要

This paper addresses the output-feedback fault-tolerant control problem for uncertain time-delay systems subject to lumped external disturbances, parametric uncertainties, and actuator failures, where full state measurements are unavailable. An output-feedback disturbance observer (DOB) is developed to estimate the lumped disturbance in real time, and a disturbance-compensation-based control law is constructed to enhance robustness without additional state sensors. By employing a Lyapunov–Krasovskii functional, delay-dependent sufficient conditions for asymptotic stability are derived in terms of linear matrix inequalities (LMIs). To enable controller synthesis, Finsler’s lemma is utilized to decouple bilinear terms, resulting in a tractable convex framework for the simultaneous computation of the observer and controller gains. Comparative simulations against PID control, sliding mode control, and active disturbance rejection control demonstrate faster convergence, smaller overshoot, and improved disturbance attenuation of the proposed method. Hardware experiments on a rotary double inverted pendulum platform further validate the effectiveness and practical applicability of the proposed approach under input time delays and actuator degradation.