Output-feedback controllers with guaranteed ℒ ₂ -gain for continuous-time Lur'e systems using noncausal Zames–Falb multipliers

This paper focuses on the problem of dynamic output feedback control for continuous-time Lur'e systems with slope-bounded nonlinearities, particularly addressing the closed-loop L2 gain. The synthesis framework is derived using integral quadratic constraints. The following contributions are highlighted: (i) assessment of stability and L2 gain through causal, anticausal, and noncausal Zames–Falb multipliers; (ii) technical enhancements to improve efficiency and to reduce the conservativeness of two different classes of multipliers regarding the L1 norm evaluation; (iii) the synthesis conditions are presented in terms of an iterative procedure based on linear matrix inequalities, allowing arbitrary order for both the controller and the multipliers. The proposed achievements are validated through numerical examples, demonstrating the efficacy and flexibility of the approach compared to existing methods in the literature.