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 del...

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Bibliographic Details
Published in:Automatica (Oxford) Vol. 46; no. 5; pp. 902 - 909
Main Authors: Li, Hongfei, Gu, Keqin
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.05.2010
Elsevier
Subjects:
Applied sciences
Channels
Computational efficiency
Computer science; control theory; systems
Control system analysis
Control theory. Systems
Coupled differential–difference equations
Delay
Exact sciences and technology
Formulations
Lyapunov–Krasovskii functional
Mathematical analysis
Mathematical models
Scalars
Time delay
Lyapunov–Krasovskii functional
Delay
Coupled differential–difference equations
Differential equation
Differential form
Coupled differential-difference equations
Lyapunov method
Multiple delay
Delay system
Difference equation
Delay equation
Occupation time
Delay time
Lyapunov―Krasovskii functional
Multiple channel
Lyapunov function
ISSN:0005-1098, 1873-2836
Online Access:Get full text
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Description
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.
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ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2010.02.007