Abstract: This work studies the problem of control design for linear systems with input saturation. It is well known that integral quadratic constraints (IQC) can be used to describe input saturation and that the use of IQC in analysis can lead to less conservative performance bound and larger domain of attraction. In this work, it is shown that a class of commonly used IQCs may not help in control synthesis. That is, the use of these IQCs does not enlarge the guaranteed domain of performance for synthesis.

Key words: integral quadratic constraints, input saturation, cost control0Introduction