Stability and Well-posedness of a Nonlinear Railway Track Model

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Date

2018-06-22

Authors

Edalatzadeh, M. Sajjad
Morris, Kirsten

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Publisher

Institute of Electrical and Electronics Engineers

Abstract

Railway tracks rest on a foundation known for exhibiting nonlinear viscoelastic behavior. Railway track deflections are modeled by a semilinear partial differential equation. This paper studies the stability of solutions to this equation in presence of an input. With the aid of a suitable Lyapunov function, existence and exponential stability of classical solutions is established for certain inputs. The Lyapunov function is further used to find an a-priori estimate of the solutions, and also to study the input-to-state stability (ISS) of mild solutions.

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Keywords

Asymptotic stability, Damping, Distributed parameter systems, flexible structures, Lyapunov methods, input-to-state stability, Mathematical model, nonlinear systems, partial differential equations, Rail transportation, Stability criteria

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