Stability problem of systems with multiple delay channels

A new form of coupled differential–difference equations with one delay in each channel is proposed to model systems with multiple delays. This formulation has significant advantage over the traditional differential–difference equations or the prevailing form of coupled differential–difference equations with multiple delays. Fundamental solutions, general solutions, and the construction of the Lyapunov–Krasovskii functional are discussed. For systems with a large number of state variables with multiple low-dimensional delay elements, this formulation allows a drastic reduction of computational cost as compared to the traditional differential–difference equation formulation when the discretized Lyapunov–Krasovskii functional method is used.