A new expression for the performance limit based on state-space representation

This paper aims to clarify the performance limit via state-space representation, in order to handle multiple-input-multiple-output systems in a transparent way. To this end, by applying some results on infinite-dimensional control theory, a closed formula for the H 2 performance limit is derived for systems with a special structure described in terms of a rational transfer matrix and a scalar inner function. This formulation is capable of dealing with various control problems, including H 2 control of a class of infinite-dimensional systems. The resulting formula, given as a functional of the inner function, helps us to understand how achievable H 2 performance deteriorates due to non-minimum phase properties or unstable modes of plants.