Robustness analysis of periodic systems

Two approaches for robustness analysis of linear periodically time-varying systems are presented. In the first approach the state space matrices of the nominal system are expanded in Fourier series. The system can then be represented as an interconnection of a linear time-invariant system and an uncertainty that contains all harmonic functions in the Fourier series. Integral quadratic constraints (IQCs) can then be used to derive robustness conditions, which are equivalent to several linear matrix inequalities. In the second approach, instead of being factorized out, the harmonic terms are kept in the nominal system. Periodic IQCs are then used to characterize the uncertainties. This generally gives a lower dimensional optimization problem but with added complexity due to the fact that the system matrices are periodic.