Pole placement of uncertain discrete systems in the smallest disk by state feedback

This paper deals with the regional pole assignment problems for uncertain discrete systems. The previous work on this area mainly focused on designing a control law to locate the closed loop eigenvalues in a specified region. In the aspect of robust performance, it is desirable that the region where the eigenvalues of the uncertain systems exist is as small as possible, because the performances of two systems with severely separated eigenvalues are much different to each other. To maintain the robust performance in this manner, the design method of this paper, first, provides the smallest circular region which can include the closed loop eigenvalues. Second, it also provides a linear state feedback which locates the eigenvalues in that region. The quadratic d-stabilizability concept is used for deriving the formulas in this paper. The proposed method is applied to uncertain systems with structured or unstructured perturbations. The linear matrix inequalities are adopted as a numerical optimization method. Illustrative examples are employed to demonstrate applications of the theory