State feedback regulation on port-Hamiltonian systems: a convex based approach

This paper focuses on the state feedback control design for a class of non-linear port-Hamiltonian systems. Attention is given for non-linear systems which can be modeled as a port-Hamiltonian systems with affine state-dependent interconnection and damping matrices, and quadratic state-dependent Hamiltonian function. In particular, an LMI based characterization of the energy balance equation is achieved. Moreover, an hyper-rectangle is established on the state space domain, attempting to maximize the domain of attraction iteratively. The proposed method is applied to the third order Lotka Volterra food chain system, with good results on the convergence to steady state at the origin.