Optimal Guaranteed-Cost Control with Pole Placement for Uncertain Systems: An LMI Approach

Abstract

Abstract The paper presents a linear matrix inequality (LMI) approach to the problem of pole placement in a specific stability region while minimizing a guaranteed cost bound for a class of uncertain systems. The uncertainty is assumed to be norm bounded and the uncertain parameters are allowed to enter both the state and the input matrices. The stability region is the intersection of a vertical strip and a disk in the open left-half complex plane. First, a state feedback controller is designed to place the closed loop poles of the uncertain system in the given stability region via any feasible solution of a corresponding LMI. Then, linear quadratic (LQ) and H measures are considered for the closed loop performance of the uncertain system. Finally, an LMI Eigenvalue Problem is proposed to select the optimal guaranteed cost controller that also satisfies the pole placement requirements. In two examples, our results are compared with the existing results.