SOLUTION TO MATRIX EQUATION AV + BW = EVF AND EIGENSTRUCTURE ASSIGNMENT FOR DESCRIPTOR SYSTEMS

A simple complete analytical restriction-free parametric solution with complete and explicit freedom of matrix equation AV + BW = EVF is presented. Based on the presented solution of this equation, an approach for eigenstructure assignment for continuous descriptor system Ex = Ax + Bu via descriptor-variable feedback u = Kx is proposed; parametric forms of the gain matrix and the eigenvectors associated with the assigned finite closed loop eigenvalues are given. The approach is shown to be better than that of Fahmy and O'Reilly (1989, Int. J. Contr., 49, 129-143) in the sense that it not only possesses the functions of the approach of Fahmy and O'Reilly (1989, Int. J. Contr., 49, 129-143), but also has the following three advantages: (1) it eliminates the requirements on the assigned finite closed loop poles; (2) it provides more design parameters; and (3) it needs less computational work.