An explicit solution to right factorization with application in eigenstructure assignment

Based on the well-known Leverrier algorithm, a simple explicit solution to right factofization of a linear system is established. This solution is expressed by the controllability matrix of the given system and a symmetric operator matrix. Applications of this solution to a type of generalized Sylvester matrix equations and the problem of parametric eigenstructure assignment by state feedback are investigated, and general complete parametric solutions to these two problems are deduced. These new solutions are simple,and possess desirable structural properties which render the solutions readily implementable. An example demonstrates the effect of the proposed results.