Parametric control of quasi-linear systems via state feedback

In the last decade, a complete parametric approach for multi-input linear systems has been proposed, which gives general parametrization of the state feedback gain, and at the same time, produces a complete parametric expression for the eigenvector matrices. In this paper, it is shown that such an approach can be generalized to a type of quasi-linear systems with coefficient matrices containing the state variables and also a time-varying parameter vector. General complete parametrization of a quasi-linear state feedback controller is proposed based on the solution to a type parameter-varying generalized Sylvester matrix equations, which gives a linear closed-loop system with desired eigenstructure. What is more, in such a realization the linear closed-loop system can often be made constant. The approach also provides all the degrees of freedom which may be further utilized to improve the system performance. An example demonstrates the proposed parametric approach.