Basic Theory for Linear Delay Equations

Abstract

For dynamical systems governed by feedback laws, time delays arise naturally in the feedback loop to represent effectS due to communication, transmission, transportation or inertia effects. The introduction of time delays in a system of differential equations results in an infinite dimensional state space. The solution operator becomes a nonself-adjoint operator acting on a Banach space of segments of functions. In this chapter we discuss the state space approach, the solution operator and its spectral properties for differential delay equations. As an application we present strong convergence results for series expansions of solutions and construct examples of solutions of delay equations that decay faster than any exponential.KeywordsFunctional Differential EquationDifferential Delay EquationCharacteristic MatrixSolution OperatorInfinitesimal GeneratorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.