Parametric Control to a Type of Quasi-Linear Descriptor Systems via Proportional Plus Derivative Feedback

Abstract

In this paper, a parametric approach for a type of quasi-linear descriptor systems in which the coefficient matrices include time-variant parameters and system variables is investigated. Inspiring by the solution of a class of generalized Sylvester matrix equations, the generally parameterized expressions of proportional-derivative feedback controller and right eigenvector matrix are established. With the proposed method, the closed-loop system can be transformed into a linear time-invariant one with expected eigenstructure. Finally, two real-world examples are presented to demonstrate the effectiveness of the proposed approach.