Estimating and enlarging the domain of attraction in IDA-PBC

Interconnection and damping assignment passivity- based control (IDA-PBC) is a nonlinear state feedback technique that endows the closed-loop system with a port-Hamiltonian (PH) structure. The assigned energy function qualifies as a Lyapunov function and thus can be used to estimate the domain of attraction (DA). However, determining the largest bounded sublevel set of a general energy function which is contained in the DA is a difficult task. In this paper, a numerical algorithm is developed to cope with this problem without formulating conditions on the energy function. Moreover, an optimization procedure is proposed to determine a controller parametrization which maximizes the estimated DA, while simultaneously taking account of desired closed-loop performance. An illustrative example is included, where also a comparison to a linear state feedback controller is presented.