Parameterized H∞ controller design for adaptative trade-off by finite dimensional LMI optimization

We consider the design of a control law K(s, θ) such that a set of trade-offs parameterized by a scalar θ are satisfied for a given LTI system. The trade-off is formulated as an optimization problem involving a weighted H∞ norm. Matrices of the state space representation of K(s, θ) have to be obtained as explicit functions of θ. This problem, close to the LPV control design, can be naturally formulated as a convex but infinite dimensional optimization problem. The contribution of this paper is to propose design methods based on finite dimensional LMI optimization problem, avoiding the “naive” gridding approach.