Solution of matching equations of IDA-PBC by Pfaffian differential equations

Finding the general solution of partial differential equations (PDEs) is essential for controller design in newly developed methods. Interconnection and damping assignment passivity-based control (IDA-PBC) one such methods which to corresponding PDEs are called matching needed apply it practice. In this paper, these transformed Pfaffian equations. Furthermore, shown that upon satisfaction integrability condition, third-order equation may be obtained quite easily. The method applied IDA-PBC some benchmark systems as Magnetic levitation system, Pendubot, underactuated cable-driven robot verify its applicability.