Incremental Stability Analysis of Lurie Systems
Lanlan Su, Ross Drummond, Sei Zhen Khong · 2024
The incremental stability analysis of Lurie systems consisting of the feedback interconnection between a linear time-invariant (LTI) system and a slope-bounded nonlinearity is considered. We first show that the incremental input-output mappings generated by the set of slope-bounded nonlinearities satisfy a set of biased integral quadratic constraints (IQCs) defined by Popov multipliers. Then, a frequency-domain inequality (FDI) condition on the LTI system is proposed for establishing incremental closed-loop stability via an incremental form of IQC theory. Application of the KYP lemma yields an equivalent linear matrix inequality (LMI) condition.