On the exponential convergence of input-output signals of nonlinear feedback systems

2022/06/04 by Su, Lanlan, Zhao, Di, Khong, Sei Zhen · 1 citation
#FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2206.01945

Abstract

This note studies the exponential convergence of input-output signals of discrete-time nonlinear systems composed of a feedback interconnection of a linear time-invariant system and a nonlinear uncertainty. Both the open-loop subsystems are allowed to be unbounded. Integral-quadratic-constraint-based conditions are proposed for these uncertain feedback systems, including the Lurye type, to exhibit the property that the endogenous input-output signals enjoy an exponential convergence rate for all initial conditions of the linear time-invariant subsystem. The conditions are established via a combination of tools, including integral quadratic constraints, directed gap, and exponential weightings.

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