GAIN-SCHEDULED CONTROL USING DYNAMIC INTEGRAL QUADRATIC CONSTRAINTS

The problem of designing a stabilizing controller for the feedback interconnection of an LTI plant, G, and a perturbation block, Δ, is investigated. The desired controller is itself an interconnection of an LTI part, C, and a perturbation block, Δc(Δ). We first give a set of necessary conditions for the existence of such a controller. The derivation of the conditions originates in the stability analysis of the closed-loop system using integral quadratic constraints (IQCs) involving dynamic multipliers. If these necessary conditions are complemented by suitable coupling constraints, they allow to construct a desired controller that stabilizes the closed-loop system with Δc = Δ. These existence conditions consist of a set of linear matrix inequalities that depend on multipliers which satisfy IQCs associated with Δ. Existing results in the literature are recovered when the multipliers are restricted to be static.