Estimate of domain of attraction for a class of Port-Controlled Hamiltonian systems subject to both actuator saturation and disturbance

Abstract

This paper investigates the estimate of domain of attraction for a class of nonlinear Port-Controlled Hamiltonian (PCH) systems subject to both actuator saturation and disturbances. Firstly, two conditions are established to determine whether an ellipsoid is contractively invariant for the systems only with actuator saturation, with which the biggest ellipsoid contained in the domain of attraction can be found and a new estimation method is presented. It is shown that the proposed conditions can be expressed in the form of the linear matrix inequality optimization problem with constraints. Secondly, the obtained conditions are extended to estimate the domain of attraction of the systems subject to both actuator saturation and disturbances, and a new estimation method is proposed. Study of an illustrative example shows that the methods proposed in this paper work very well in estimating the domain of attraction for some classes of nonlinear PCH systems with actuator saturation and/or disturbances.