Robustness analysis of continuous periodic systems using integral quadratic constraints

A general approach to analyze the robust performance and robust stability via the worst-case input/output gain for uncertain, linear time periodic systems is presented. The input/output behavior of the uncertain block is described by an integral quadratic constraint. A dissipation inequality is derived to compute an upper bound for this gain. The worst-case gain condition can be formulated as a semidefinite program and the result can be interpreted as a Bounded Real Lemma for uncertain linear periodic systems. The effectiveness of the proposed method is demonstrated on a realistic numerical example of a controlled wind turbine.