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Steady-state analysis of networked epidemic models
In this paper, we develop two positive feedback frameworks that are applicable to the study of steady-state values in a wide range of compartmental epidemic models, including both group and networked processes.
On the exponential convergence of input-output signals of nonlinear feedback systems
We show that the integral-constraint-based robust feedback stability theorem for certain Lurye systems exhibits the property that the endogenous input-output signals enjoy an exponential convergence rate for all initial conditions of the linear time-invariant subsystem.
On the Necessity and Sufficiency of Discrete-Time O'Shea-Zames-Falb Multipliers
Roughly speaking, a successful proof of the conjecture would require: (a) a conic parameterization of a set of multipliers that describes exactly the set of nonlinearities, (b) a lossless S-procedure to show that the non-existence of a multiplier implies that the Lurye system is not uniformly robustly stable over the set of nonlinearities, and (c) the existence of a multiplier in the set of multipliers used in (a) implies the existence of an LTI multiplier.
On the Necessity and Sufficiency of the Zames-Falb Multipliers for Bounded Operators
Lastly, when restricted to be LTI, the second class is demonstrated to be a subset of the third, and the existence of a Zames-Falb multiplier is shown to be sufficient but not necessary for the robust feedback stability.
