A new expression for the H2 performance limit based on state-space representation

In this paper, by applying some results on infinite-dimensional control theory, a closed formula for the H² performance limit is derived for systems that can be expressed as a series connection of a rational transfer matrix and a scalar inner function. This formulation is capable of dealing with various control problems, including H² 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 H² performance deteriorates due to non-minimum phase properties of the plants. This paper also aims to clarify the performance limit via state-space representation, in order to handle multiple-input-multiple-output systems in a transparent way.