An LMI solution for a class of robust open-loop problems

The robust filter design and the robust feedforward controller design are particular cases of a larger class of problems: the robust open-loop problems. In this article, we consider a class of uncertain open-loop plants, where a filter needs to be designed to ensure that the plant satisfies chosen specifications. The representation of uncertainties is made in a very general framework: the Linear Fractional Transformation (LFT). Associated with the Dynamic Integral Quadratic Constraints framework, it allows the consideration of many classes of structured uncertainties. This paper proves that the design of a filter ensuring a robust L
₂
-gain or H
₂
performance for the complete plant can be expressed as a convex optimization problem involving Linear Matrix Inequalities Constraints which can be solved using an efficient algorithm.