Discretized Lyapunov-Krasovskii functional for coupled differential-difference equations with multiple delay channels

Many practical systems have a large number of state variables, but only a few components involve time delays. These components are often scalar or low dimensional, and typically only one delay is present in each such component. A special form of coupled differential-difference equations with one delay per channel proposed recently is well suited to formulate such systems. This article extends the discretized Lyapunov-Krasovskii functional method to this class of systems. In addition to generality, this formulation also drastically reduces the computational cost for a typical system, and therefore is appropriate to use even for time-delay systems of retarded type. The discretized formulation is also simpler than the previous formulation for systems with multiple delays.