Asymptotic gain results for attractors of semilinear systems

2019/09/13 by Schmid, Jochen, Kapustyan, Oleksiy V., Dashkovskiy, Sergey
#Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1909.06302

Abstract

We establish asymptotic gain along with input-to-state practical stability results for disturbed semilinear systems w.r.t. the global attractor of the respective undisturbed system. We apply our results to a large class of nonlinear reaction-diffusion equations comprising disturbed Chaffee--Infante equations, for example.

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