Forward Euler Solutions and Weakly Invariant Time-Delayed Systems

Norma L. Ortiz-Robinson and Vinicio R. Ríos

Abstract and Applied Analysis, 2012, vol. 2012, 1-15

Abstract:

This paper presents a necessary and sufficient condition for the weak invariance property of a time-delayed system parametrized by a differential inclusion. The aforementioned condition generalizes the well-known Hamilton-Jacobi inequality that characterizes weakly invariant systems in the nondelay setting. The forward Euler approximation scheme used in the theory of discontinuous differential equations is extended to the time-delayed context by incorporating the delay and tail functions featuring the dynamics. Accordingly, an existence theorem of weakly invariant trajectories is established under the extended forward Euler approach.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:481853

DOI: 10.1155/2012/481853

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