On the stability of coupled delay differential and continuous time difference equations

A Liapunov type stability analysis for coupled delay differential and continuous time difference equations is given. Such systems are encountered as the internal dynamics of input output linearized non-linear time delay systems. They appear also in lossless propagation models, in economics, in gas dynamics. The main contribution of the paper is a two steps algorithm for the stability analysis of such systems. At the first step only L₂ stability is checked, while at the second step the Liapunov stability of the difference part of the system is analyzed. In these two steps, the stability of the whole system can be checked. Using this method we show the stability of a system (dependent on delay), for which the known methods in literature are inconclusive.