Robust Pole Assignment in a Specified Disk

This paper presents a method to assign robustly the closed loop system's poles in a specified disk by a state feedback for a linear time invariant system with structured or unstructured uncertainties. THe proposed robust design procedure includes two steps. Firstly, the perturbed closed loop matrix $A_{cl p}$ = $A_{cl}$ + Δ$A_{cl}$ is rearranged such that it is a function of the nominal closed loop matrix $A_{cl}$. Hence, we can control the positions of the perturbed closed loop poles by choosing $A_{cl}$ appropriately. Secondly, the feedback control law F that assigns the closed loop poles of the perturbed system in a specified disk is determined from the equation $A_{cl}$ = A + BF. A procedure for finding F is proposed based on partitioning every matrix of the equation $A_{cl}$ = A + BF in the horizontal direction.