Robust eigenvalue placement optimization for high-order descriptor systems in a union region with disjoint discs based on harmony search algorithm

Abstract

In this paper, a new optimization scheme is proposed for robust eigenvalue placement in high-order descriptor systems in union region based on harmony search algorithm. The specification on the closed-loop eigenvalues is given in terms of robust union region stability constraints. The radius or the position of the subregions can be arbitrarily specified in complex plane for the transient performance request. By using exact eigenvalue placement theory and combining the harmony search algorithm, the robust eigenvalue placement for high-order descriptor linear system in union region is converted into a global dynamical optimization problem. Further, the eigenstructure of the closed-loop system matrix can be optimized with better robustness bound (i.e., the spectral upper bound of the maximum allowable perturbation or uncertainty for the system matrices) by the proposed scheme without imposing restriction on the differentiability of the nonlinear robust measure index function. Consequently, the robust feedback controller can be obtained by dynamically optimizing the eigenvalue and eigenvector pairs of the system. Finally, the simulation results illustrate the effectiveness and superiority of the proposed method.