Direct parametric control of fully-actuated second-order nonlinear systems—descriptor 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 second-order nonlinear systems in descriptor forms. It is revealed that, with this proposed direct parametric approach, a fully-actuated descriptor system, no matter linear or nonlinear, can actually be turned, by a set of state proportional plus derivative feedback controllers, into a linear descriptor system with the dynamical part of the system being a constant linear one with a desire eigenstructure. A general complete parametric expression for all such controllers is established based on the solution to a type of fully-actuated second-order Sylvester matrix equations. What is more, in such a realization the approach also provides all the degrees of freedom which are represented by three parameter matrices and may be further utilized to improve the system performance.