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<p>In this paper, the stability problem of a class of linear system coupling heat equations which is unstable with pulse width modulation (PWM) control input is studied. Firstly, the duty cycle scheme is designed according to the overall state to realize the stability of the coupling system. During each duty cycle, the amplitude of the pulse is fixed. Secondly, we use Lyapunov functional technique and backstepping method to prove the stability of the coupling system of ordinary differential equation and classical heat equation. Finally, we give a numerical example of a PDE-ODE coupled system to illustrate the validity of our theoretical results.</p>

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The PWM Control of a Linear System Coupled a Heat Equation

  • 期刊论文

  • 发表日期：

    2025年10月18日

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  • Zhenhui Xu,
  • Xiju Zong

摘要

In this paper, the stability problem of a class of linear system coupling heat equations which is unstable with pulse width modulation (PWM) control input is studied. Firstly, the duty cycle scheme is designed according to the overall state to realize the stability of the coupling system. During each duty cycle, the amplitude of the pulse is fixed. Secondly, we use Lyapunov functional technique and backstepping method to prove the stability of the coupling system of ordinary differential equation and classical heat equation. Finally, we give a numerical example of a PDE-ODE coupled system to illustrate the validity of our theoretical results.