Edalatzadeh, M. SajjadMorris, Kirsten2018-07-162018-07-162018-06-22https://doi.org/10.1109/LCSYS.2018.2849831http://hdl.handle.net/10012/13482© 2018 IEEE.Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.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.enAsymptotic stabilityDampingDistributed parameter systemsflexible structuresLyapunov methodsinput-to-state stabilityMathematical modelnonlinear systemspartial differential equationsRail transportationStability criteriaArticle