Robust pole assignment in matrix descriptor second-order linear systems

Abstract

The present paper considers eigenvalue assignment with minimum sensitivity in matrix descriptor second-order linear (MDSOL) systems via proportional-derivative plus partial second-derivative state feedback. Based on a result in the perturbation theory of the eigenvalue problem of MDSOL systems, a closed-loop eigenvalue sensitivity measure in terms of the closed-loop normalized right and left eigenvectors is established directly in the matrix second-order framework. Also a general parametric eigenstructure assignment for MDSOL systems via proportional-derivative plus partial second-derivative state feedback is proposed. Based on this, the robust pole assignment problem is converted into an independent minimization problem. The closed-loop eigenvalues may be easily taken as part of the design parameters and optimized within certain desired fields on the complex plane to improve robustness. Using a simple sequential-order 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 mass-spring system demonstrates the effect of the proposed approach.