Minimax controller design for a class of uncertain linear systems
The paper presents results on the design of minimax controllers for a class of uncertain linear systems. The system is subject to disturbance inputs which are related to the disturbance outputs by a system representing the structured uncertainty. Each uncertainty input is bounded by an integral quadratic constraint. The system performance is measured by an integral quadratic cost function. The results are closely related to that of \textit{A. V. Savkin} and \textit{I. R. Petersen} [IEEE Trans. Autom. Control, AC-39, 1971-1977 (1995; Zbl 0829.49003)]. The present paper gives a new proof of minimax optimality. It is shown that, to design a minimax controller, an objective function dependent upon the solution of a parametric Riccati equation has to be optimized with respect to the parameters. This objective function is shown to be convex over the set of feasible parameters. The application of the proposed method is illustrated by a numerical example.
scientific article; zbMATH DE number 1331861
scientific article