Abstract In this paper, the stabilization and H ∞ control are considered for switched port-controlled Hamiltonian systems (SPCHSs) with unstabilizable modes via energy-based multiple Lyapunov functions (MLFs) methods and mode-dependent average dwell time (MDADT) strategies, where an improved MDADT-based tradeoff method is developed by a time subsequence technique to govern the running time of the asymptotic stabilization modes and the other ones. Firstly, based on the mode-dependent state feedback controllers, stabilization conditions are derived for SPCHSs with unstabilizable modes under a new MDADT scheme. Secondly, for the case that there are external disturbances for the system, the mode-dependent H ∞ controllers are designed to attenuate external disturbances, besides, H ∞ control conditions are achieved for the system by the energy-based MLFs method with the designed MDADT scheme. Finally, two simulation examples are presented to demonstrate the effectiveness of the proposed methods.

中文翻译：

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具有不稳定模式的切换端口控制的哈密顿系统的控制设计：一种改进的依赖模式的平均驻留时间方案

摘要 在本文中，通过基于能量的多李雅普诺夫函数 (MLFs) 方法和依赖于模式的平均驻留时间 (MDADT) 策略，考虑了具有不稳定模式的切换端口控制哈密顿系统 (SPCHS) 的稳定性和 H ∞ 控制，其中通过时间子序列技术开发了一种改进的基于 MDADT 的权衡方法，以控制渐近稳定模式和其他模式的运行时间。首先，基于依赖于模态的状态反馈控制器，在新的MDADT方案下推导出具有不稳定模态的SPCHS的稳定条件。其次，对于系统存在外部扰动的情况，设计了模态相关的 H ∞ 控制器来衰减外部扰动，此外，系统的 H ∞ 控制条件是通过基于能量的 MLFs 方法与设计的 MDADT 方案实现的。最后，给出了两个仿真例子来证明所提出方法的有效性。