Solutions of the Equation AV + BW = VF and Their Application to Eigenstructure Assignment in Linear Systems

Two new simple, complete, analytical, and restriction-free solutions with complete and explicit freedom of the matrix equation AV + BW = VF are proposed. Here [A B] is known and is controllable, and F is in the Jordan form with arbitrary given eigenvalues. Based on the proposed solutions of this matrix equation, a complete parametric approach for eigenstructure assignment in linear systems via state feedback is proposed, and two new algorithms are presented. The proposed solutions of the matrix equation and the eigenstructure assignment result are generalizations of some previous results and are simpler and more effective.