Matrix criterion robust linear quadratic control problem

Abstract

This paper studies a robust linear quadratic (LQ) control problem with multiple quadratic performance indices. Specifically, a linear model is assumed to be available for each of a prespecified set of operating points of a system. A vector-valued quadratic control performance index is given at each operating point. It is then desired to find the constant feedback gains of a linear controller to obtain satisfactory control performance over all the operating points. This is a realistic case involving the minimization of a vector criterion of vector criteria, i.e. a matrix-valued criterion. The matrix-valued criterion gives insight into standard robust LQ design, and leads to several related vector minimization problems, and to natural procedures for computing a satisfactory non-inferior solution to the matrix-valued minimization problem.