Research Article On the Parametric Solution to the Second-Order Sylvester Matrix Equation EVF2−AVF −CV = BW

This paper considers the solution to a class of the second-order Sylvester matrix equa-tion EVF2−AVF −CV = BW. 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 effective-ness of the proposed solution. Copyright © 2007 Wang Guo-Sheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1