A constructive approach for the parametrization of interconnection and damping assignment passivity based control

When a port-Hamiltonian system is a result of state feedback control, as it is the case for interconnection and damping assignment passivity based control (IDA-PBC), the intuitive choice of the design parameters in the interconnection and damping matrices is often impeded by a complicated energy function. In our contribution we present a systematic approach to fix constant parameters of the design matrices of IDA-PBC, such that the closed loop system behaves like a linear sample system in the environment of the assigned equilibrium, while (nonlinear) asymptotic stability is guaranteed with the standard IDA-PBC arguments. As a further result we give conditions under which a simplified, e.g., linearized control law can be applied, preserving stability of the closed loop nonlinear system.