Robust partial eigenvalue assignment of second order descriptor systems

Abstract

Partial eigenvalue assignment problem (PEAP) of second order descriptor systems is investigated by using acceleration–velocity–displacement feedback. First, we derive parametric expressions of the solutions to the PEAP of a second order descriptor system, i.e., giving the expressions of acceleration, velocity and displacement feedback matrices such that the closed-loop system is regular and has the index at most 1, and some eigenvalues of the open-loop system are replaced by the desired ones, and the other eigenpairs of the open-loop system are kept unchanged. Then a numerical method is proposed for robust partial eigenvalue assignment of a second order descriptor system so that the closed-loop system is as robust as possible. Our method avoids to use the unchanged eigenpairs of the open-loop system and it is effective whether the closed-loop system has infinite eigenvalue or not. Numerical experiments are reported to test the efficiency of the proposed method.