Continuity Properties of LQG

It is shown that the LQG optimal controller is a continuous function of the plant. The result is proved for a class of plants which contains the class of strictly proper nite-dimensional plants. The topology employed is the one generated by convergence of the closed loop transfer functions in an induced L 1 sense. This topology is slightly stronger than the usual (H 2) gap metric convergence on transfer functions. Notation R and C denote the real and complex elds. H 2 , H 1 denote the standard Hardy spaces in the right half of the complex plane. L p denotes the standard Lebesgue space and k k p its norm. If G(s) is a matrix function of s, G (s) := G(?s) 0 is the conjugate of G(s). If G(s) is real rational, G (s) = G(?s) 0. H n p , L n p etc. denote corresponding spaces of vector-valued functions. We denote by + the orthogonal projection from L n 2 (?j1; j1) onto H n 2. Dimensions will be suppressed if they can be inferred from the context.