Parametric control to a type of quasi-linear high-order systems via output feedback

This paper investigates the design problem of output feedback control to a type of quasi-linear high-order systems containing time-variant coefficient matrices which include time-variant parameters and system variables. Based on the solution to a class of high-order generalized Sylvester matrix equation, we can design the left and right closed-loop eigenvectors and obtain two groups of arbitrary parameters, further establish a general complete parametrized expression for a quasi-linear high-order output feedback controller. By the presented parametric approach, the closed-loop system can be transformed into a linear time-invariant one with the desired eigenstructure. Finally, a nonlinear feedback synchronization problem of Genesio-Tesi and Coullet chaotic systems is presented to prove the effectiveness of the proposed approach.