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Discretized Lyapunov-Krasovskii functional for coupled differential-difference equations with multiple delay channels. (English) Zbl 1191.93120
Summary: 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.

##### MSC:
 93D05 Lyapunov and other classical stabilities (Lagrange, Poisson, $$L^p, l^p$$, etc.) in control theory 93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) 34K20 Stability theory of functional-differential equations 65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
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