Memristor‐based disturbance rejection control for port‐Hamiltonian systems with locally fixed‐time convergence

Abstract

The memristor is added to the port-Hamiltonian systems to improve the disturbance suppression performance in this paper. The concepts of locally fixed-time stability and locally fixed-time H ∞ $H_{\infty }$ control of port-Hamiltonian systems are presented. From this starting point, two novel memristor-based locally fixed-time controllers are designed to suppress the external disturbance of port-Hamiltonian systems via the interconnection and damping assignment passivity-based control technique. Comparing with the classical interconnection and damping assignment passivity-based control methodology without memristor, there are some advantages. First, the settling-time related to the memristor-based controllers in stabilizing the same port-Hamiltonian systems are shorter. Second, the memristor-based controllers can make the oscillation in the case of the strong periodic disturbance be better suppressed. Theoretical analysis shows that the memristor-based controller possesses good disturbance rejection performance owing to it can make the system states in a neighbourhood accelerate convergence to the desired equilibrium point. Two illustrative examples show that the theoretical results and the controllers designed in this paper work very well.