On the Parametric Solution to the Second-Order Sylvester Matrix Equation EVF~2 -AVF-CV=BW

摘要

This paper considers the solution to a class of the second-order Sylvester matrix equation EVF~2 - AVF - CV = B W. Under the controllability of the matrix triple (E,A,B), a complete, general, and explicit parametric solution to the second-order Sylvester matrix equation, with the matrix F in a diagonal form, is proposed. The results provide great convenience to the analysis of the solution to the second-order Sylvester matrix equation, and can perform important functions in many analysis and design problems in control systems theory. As a demonstration, an illustrative example is given to show the effectiveness of the proposed solution.