On the matching equations of kinetic energy shaping in IDA-PBC

Interconnection and damping assignment passivity-based control scheme has been used to stabilize many physical systems such as underactuated mechanical through total energy shaping. In this method, some partial differential equations (PDEs) related kinetic potential shaping shall be solved analytically. Finding a suitable desired inertia matrix the solution of nonlinear PDEs relevant is challenging problem. paper, systematic approach solving matching equation for with one degree underactuation proposed. A special structure proposed simplify corresponding PDE. It shown that method more general than reported methods in literature. order derive matrix, necessary condition also derived. The applied three examples, including pendubot, VTOL aircraft, 2D SpiderCrane.