Large systems with multiple low-dimensional delay channels

This article discusses the stability problem of systems with multiple delay channels. The problem is formulated in the form of coupled differential-difference equations with single independent delay in each channel. However, systems with multiple independent or dependent delays in some channels can be transformed into the standard form. Fundamental solutions, the stability of difference equations, and the construction of Lyapunov-Krasovskii functional are discussed. It is concluded that the formulation has substantial advantage over the traditional formulation, especially for systems with a large number of state variables with multiple low dimensional delay channels.