Solution to the Equation MVF2 + DVF + KV = BW – The Nonsingular Case

G.-R. Duan and B. Zhou (PRC)


Second-order Sylvester matrix equations, right factoriza tion, general solutions, degree of freedom, controllability.


This note provides a complete general parametric solution to the generalized second-order Sylvester matrix equation MV F2 + DV F + KV = BW, with M nonsingular and F being an arbitrary known matrix. The primary feature of this solution is that the matrix F does not need to be in any canonical form, or may be even unknown a priori. The results provide great convenience to the computation and analysis of the solutions to this class of equations, and can perform important functions in many analysis and design problems involving second-order dynamical systems.

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