Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 55, Issue 2, Pages 554-559Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2009.2038196
Keywords
Backstepping; delay systems; distributed parameter systems
Funding
- National Science Foundation (NSF)
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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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