The Testing for Optimally of Linear Systems†

Abstract

Procedures exist for designing optimal linear controllers for linear systems subjected to additive noise at the input and output. The paper considers the inverse problem of deciding whether a given controller, specified by its transfer function, is optimal for a prescribed linear plant. A closed form test for optimality is derived for single input, single output plants, while for all other situations the testing for optimality is reduced to the derivation of a non-singular solution of a prescribed quadratic matrix equation.