Direct parametric control of fully-actuated high-order nonlinear systems—Normal case

Full-actuation of a dynamical system really provides great potential for system control, and yet this potential is seldom utilized or even recognized. In this paper, the direct parametric approach for fully-actuated second-order nonlinear systems recently proposed is generalized to the case of fully-actuated high-order nonlinear systems. It is revealed that, with this proposed direct parametric approach, a fully-actuated system, no matter linear or nonlinear, can actually be turned into a constant linear system with desire eigenstructure by a state proportional plus derivative feedback controllers, and a general complete parametric expression for all such controllers are established based on the solution to a type high-order Sylvester matrix equations. What is more, in such a realization the approach also provides all the degrees of freedom which may be further utilized to improve the system performance.