Direct parametric control of fully-actuated high-order quasi-linear systems via dynamical feedback

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, a direct parametric approach for dynamical feedback control of fully-actuated high-order quasi-linear systems with derivative terms of the control input is proposed. Both the normal case and the descriptor case are considered. It is revealed that, with this proposed direct parametric approach, a fully-actuated system, no matter linear or nonlinear, can be turned by a dynamical feedback controller into a linear system whose dynamical part is a constant one with a desire eigenstructure. A general complete parametric expression for the coefficients of such controllers is established. 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.