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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,...
In a previous work, we presented formulae for boundary control laws which stabilized the parabolic profile of an infinite channel flow, linearly unstable for high Reynolds number. Also know as the Poiseuille flow, this problem is frequently cited as a paradigm for transition to turbulence, whose stabilization for arbitrary Reynolds number, without using discretization, had so far been an open problem...
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