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. (C) 2010 Elsevier Ltd. All rights reserved.