Robust pole assignment in descriptor systems via proportional plus partial derivative state feedback

Abstract

The problem of eigenvalue assignment with minimum sensitivity in multivariable descriptor linear systems via proportional plus partial derivative state feedback is considered. Different from the purely proportional state feedback case, the number of finite closed-loop eigenvalues is required to be equal to the system dimension. Based on a result in the perturbation theory of generalized eigenvalue problem of matrix pairs, the closed-loop eigenvalue sensitivity measures in terms of the closed-loop normalized right and left eigenvectors are established. By combining these measures and a recently proposed general parametric eigenstructure assignment result for descriptor linear systems via proportional plus derivative state feedback, the robust pole assignment problem is converted into an independent minimization problem. A simple algorithm in sequential order is obtained for solution to the problem of robust pole assignment in descriptor linear systems via proportional plus partial derivative state feedback. The closed-loop eigenvalues may be easily taken as a part of the design parameters and optimized within certain desired fields on the complex plane to improve robustness. Using the proposed algorithm, the optimality of the obtained solution to the robust pole assignment problem is totally dependent on the solution to the independent minimization problem. An example of order six is worked out with multiple solutions, both the indices and the numerical robustness test demonstrate the effect of the proposed approach.