Spectral Analysis for Delay Differential-Algebraic Systems

The aim of this paper is the study of the stability properties of a class of systems expressed by functional differential equations coupled with difference equations. Starting by the linear case, we extend the spectral projection methodology for Lossless systems by introducing an appropriate bilinear form. A sufficient criteria for convergence of series expansion for the considered system is established. For the nonlinear case, the center Manifold theorem is extended to functional differential equations coupled with difference equations leading to reducing the dimension of the initial system. Finally, we illustrate the obtained results by computational example.