Stabilization via output feedback for a type of uncertain time-varying port-controlled Hamiltonian system based on linear matrix inequality approach

In this paper, the control of a type of uncertain time-varying port-controlled Hamiltonian (PCH) systems is investigated. As a matter of fact, the control method proposed in this paper is not based on passivity of PCH systems, but a general output equation is introduced inspired by the measured “information” in the systems in traditional control system theory and the problem of output feedback is considered. In this paper, a conception of p-quadratic stability of the type of PCH system is introduced, and the relationship between p-quadratic stability and Lyapunov stability is pointed out. Then, the problem for p-quadratic stabilization of the proposed system via static output feedback is solved in the following two cases, respectively. For the case of unperturbed output equation, a necessary and sufficient condition for the problem is derived in terms of two groups of linear matrix inequalities (LMIs); for the general case that the output equation also has time-varying perturbations, a sufficient condition for p-quadratic stable of closed-loop system is also given in terms of LMIs. It is also shown that conservatism can be greatly reduced when the perturbation variables in the uncertain PCH systems are restricted to vary within certain intervals. Finally, a numerical example is proposed in the end followed by a simulation to verify the effectiveness of the method proposed in this paper.