The Properties of an Output Feedback Scheme and Control System Design. Approach from Low-Order Model.

Abstract

The optimal regulator is a key device in modern linear control theory. This paper deals with a problem of computation of the output feedback gain which minimizes the quadratic performance criterion. Numerous methods of computation of the output feedback have been presented in other reports, but they all require iterative calculation. However, use of such iterative algorithms requires solution of nonlinear matrix equations. Furthermore, the conditions for the existence of the output feedback gain which satisfies an algebraic equation are unclear. In this paper, a low-order model for computation of the feedback gain is proposed. This method is based on the second method of Lyapunov. The computational method for the output feedback gain and comparison of the Lyapunov functions of the original system and the low-order model are presented. This computational procedure does not involve use of any iterative algorithms. We have identified the conditions for the existence of the output feedback gain and the sufficient conditions for attainment of the optimal solution.