Analysis of Lur’e dominant systems in the frequency domain

Abstract

Frequency domain analysis of linear time-invariant (LTI) systems in feedback with static nonlinearities is a classical and fruitful topic of nonlinear systems theory. We generalize this approach beyond equilibrium stability analysis with the aim of characterizing feedback systems whose asymptotic behavior is low dimensional. We illustrate the theory with a generalization of the circle criterion for the analysis of multistable and oscillatory Lur'e feedback systems.

Antithetic integral feedback for the robust control of monostable and oscillatory biomolecular circuits

“…The theory takes nonlinear models with parameters in a certain range and characterizes their behavior through Lyapunov-like linear matrix inequalities (LMIs). Dominance theory was introduced in Forni and Sepulchre (2019); Miranda-Villatoro et al (2018a) to study systems that have several equilibria or that oscillate. The intuition for the theoretical framework is that the dynamics of a p-dominant systeṁ ξ = f (ξ) ξ ∈ R n (5) can be split into fading sub-dynamics of dimension n − p and dominant sub-dynamics of dimension p, constraining the system's steady-state behavior.…”

Qualitative behavior and robustness of dendritic trafficking

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Differentially passive circuits that switch and oscillate

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