A New Expression for the Discrete Time H2 Performance Limit based on State-Space Representation

In this paper, we derive an analytical expression of the H
²
performance limit based on state space representation. In order to focus on effects of non-minimum phase properties, we express systems as a series connection of a rational transfer matrix and a scalar inner function. The final result, given as a functional of the inner function, helps us to understand how achievable H
²
performance deteriorates due to non-minimum phase properties of the plants