IEEE Transactions on Automatic Control · 2010 · 299 citations · 23 references
EngineeringMathematicsSystems EngineeringDynamical SystemsSensorsSystem DynamicsControl Of Dynamical SystemsControl SystemsControl TheoryFeedback ControlStability TheoryTime Delay EffectsClosed-loop StabilityExponential StabilityFeedback DesignInput Delay SystemsLinear Time-invariant SystemsLyapunov StabilityLyapunov Stability AnalysisLyapunov Stability Theory
For linear time-invariant systems with a time-varying input delay, an explicit formula for predictor feedback was presented by Nihtila in 1991. In this note we construct a time-varying Lyapunov functional for the closed-loop system and establish exponential stability. The key challenge is the selection of a state for a transport partial differential equation, which has a non-constant propagation speed, and which is the basis of the stability analysis. We illustrate the design and its conditions with several examples. We also develop an observer equivalent of the predictor feedback design, for the case of time-varying sensor delay.
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