Application of matrix perturbation theory in robust control of large-scale systems

The aim of this paper is to develop new results for robust centralized and decentralized control of large-scale systems using matrix perturbation theory. A new robustness measure is proposed which is more appropriate for large-scale systems than the existing measures. The use of this new index allows for an evaluation of system eigenvalue sensitivity to perturbations without calculating the eigenvectors and the condition number of the modal matrix. In addition, a novel robust decentralized controller design method is proposed to assign the closed-loop eigenvalues of the large-scale system in a desired region. This method is based on eigenstructure assignment of isolated subsystems. The assignment of overall closed-loop poles in the desired region is guaranteed provided that certain sufficient conditions for the isolated subsystems are satisfied. Simulation results are given to show the efficiency of the new methods.