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Robustness analysis of eventually periodic systems using integral quadratic constraints with periodic multipliers

Robustness analysis with integral quadratic constraints (IQCs) using periodically time-varying multipliers is considered in this work. A sufficient condition akin to standard IQC analysis is presented, with the possibility that the nominal system is eventually periodic and the IQC multipliers are periodic. This result is made possible by using a dissipativity-based proof for IQC analysis and requiring a certain structure on IQC multipliers. The crux of the proof depends on the existence of a periodic stabilizing solution to the discrete difference Riccati equation. By using a descriptor, time-invariant representation of the periodic system, the IQC analysis results follow.