Parametric eigenstructure assignment via output feedback based on singular value decompositions

Eigenstructure assignment in multivariable linear systems via output feedback is investigated. Three problems are proposed that are related to a type of generalised Sylvester matrix equations. By proposing a general complete parametric solution to this type of generalised Sylvester matrix equations based on singular value decompositions, a general complete parametric approach is 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 utilised to achieve desired specifications. Based on the proposed results and the Matlab Optimisation Toolbox, a Matlab file is created, which finds a solution that gives minimum closed-loop eigenvalue sensitivities for the problem of eigenstructure assignment via output feedback.