Parametric eigenstructure assignment via output feedback based on singular value decompositions

This paper investigates eigenstructure assignment in multivariable linear systems via output feedback. Three problems are proposed and are related to a type of generalized Sylvester matrix equations. By proposing a general complete parametric solution to this type of generalized Sylvester matrix equations based on singular value decompositions, a general complete parametric approach is then presented for the proposed eigenstructure assignment problems. General parametric expressions for both the closed-loop eigenvector matrices and the output feedback gain are established in terms of certain parameter vectors. These parameter vectors provide the design degrees of freedom and can be utilized to achieve some desired specifications. Bases on the proposed results and the Matlab Optimization Toolbox, a Matlab file is created, which finds for the problem of eigenstructure assignment via output feedback a solution that gives minimum dosed-loop eigenvalue sensitivities.