Low-frequency robust control for singularly perturbed system

This study is concerned with the low-frequency (LF) integral quadratic constraints (IQC) of the linear singularly perturbed model (SPM). The conditions satisfying LF IQC are derived in terms of linear matrix inequalities by using the generalised Kalman–Yakubovich–Popov lemma. As special cases of LF IQC, LF bounded realness and LF positive realness are exploited in detail. In addition, upper bound of the small perturbation parameter, which relates to the robustness of SPM, can be estimated. Numerical simulations demonstrate that the proposed method can reduce the conservatism and characterise the SPM more specifically by ignoring the unrelated frequency range.