Stabilisation and ℋ∞ control for switched port-controlled Hamiltonian systems with unstable modes and actuator saturation

In this paper, the problems of stabilisation and $\mathcal {H}_\infty $H∞ control are addressed for switched port-controlled Hamiltonian (SPCH) systems with unstable modes and actuator saturation (AS) via energy-based multiple Lyapunov functions methods. Firstly, by a switching state feedback controller with truncation-inequality techniques, the considered system is transformed into an unforced SPCH system with asymptotically stable, stable and unstable modes. Then, by developing an alternative switching law with slow/fast mode-dependent average dwell time (MDADT) switching scheme, new sufficient conditions are obtained for stabilisation of the SPCH system. Secondly, by designing a new switching $\mathcal {H}_\infty $H∞ feedback controller, revealing the characteristics of alternative switching signals and defining an indicative function, a new criterion for $\mathcal {H}_\infty $H∞ control of the SPCH systems with unstable modes and AS is achieved via the slow/fast MDADT switching scheme. Moreover, based on the obtained results and the indicative function, $\mathcal {H}_\infty $H∞ control conditions for the corresponding SPCH system are also derived under a slow MDADT switching scheme and a traditional average dwell time scheme, respectively. Finally, some numerical examples are given to verify the effectiveness of the proposed methods.