Robust pole assignment in descriptor linear systems via state feedback

The problem of eigenvalue assignment with minimum sensitivity in multivariable descriptor linear systems via state feedback is considered. Based on the perturbation theory of generalized eigenvalues of matrix pairs, the sensitivity measures of the closed-loop finite eigenvalues are established in terms of the closed-loop normalized right and left eigenvectors. By combining these measures with a recently proposed general parametric eigenstructure assignment result for descriptor linear systems via state feedback, the robust pole assignment problem is converted into an independent minimization problem. The optimality of the obtained solution to the robust pole assignment problem is totally dependent on the solution to the independent minimization problem. The closed-loop eigenvalues are also taken as a part of the design parameters and are optimized, together with the other degrees of freedom, within certain desired regions on the complex plane. The approach takes numerical stability into consideration and also gives good robustness for the closed-loop regularity.