Robustness analysis of linear parameter varying systems using integral quadratic constraints

A general approach is presented to analyze the worst case input/output gain for an interconnection of a linear parameter varying (LPV) system and an uncertain or nonlinear element. The input/output behavior of the nonlinear/uncertain block is described by an integral quadratic constraint (IQC). A dissipation inequality is proposed to compute an upper bound for this gain. This worst-case gain condition can be formulated as a semidefinite program and the result can be interpreted as a Bounded Real Lemma for uncertain LPV systems. The paper shows that this new condition is a generalization of the well known Bounded Real Lemma for LPV systems. The effectiveness of the proposed method is demonstrated on a simple numerical example.