Pole Allocation using Matrix Perturbations

An approach is presented for the analysis and design of controllers and observers for high-dimensional systems using pole allocation and matrix perturbation theory. Development of a feedback control law that leads to a desired closed-loop configuration is a prohibitive task computationally, especially for large-order systems. Existing pole allocation algorithms can handle only low-order models. In this paper, matrix perturbation theory is used to provide an estimate of the system eigensolution, which is consequently used to analyze and design the closed-loop controller. The accuracy of the control (or observer) design depends on how small a perturbation the controls (or observer gains) are on the uncontrolled system, and it is assessed qualitatively by considering Gerschgorin's disks and the system eigensolution.