Pole placement of uncertain discrete systems in the smallest diskby state feedback

摘要

This paper deals with the regional pole assignment problems foruncertain discrete systems. The previous work on this area mainlyfocused on designing a control law to locate the closed loop eigenvaluesin a specified region. In the aspect of robust performance, it isdesirable that the region where the eigenvalues of the uncertain systemsexist is as small as possible, because the performances of two systemswith severely separated eigenvalues are much different to each other. Tomaintain the robust performance in this manner, the design method ofthis paper, first, provides the smallest circular region which caninclude the closed loop eigenvalues. Second, it also provides a linearstate feedback which locates the eigenvalues in that region. Thequadratic d-stabilizability concept is used for deriving the formulas inthis paper. The proposed method is applied to uncertain systems withstructured or unstructured perturbations. The linear matrix inequalitiesare adopted as a numerical optimization method. Illustrative examplesare employed to demonstrate applications of the theory