Delay Systems
By Sébastien Boisgérault, MINES ParisTech
August 18, 2017
Contents
About
Systems of delay-differential algebraic equations (DDAE) – or delay systems for the sake of brevity – combine differential and algebraic equations with delayed variables in the right-hand side. A typical example1 would be: \[ \begin{array}{rll} \dot{x}(t) &=& E x(t) - FG y(t) \\ y(t) &=& \displaystyle e^{T E} x(t-T) - \int_{-T}^0 e^{-\theta E} FG y(t+\theta) d\theta \end{array} \]
Presentations
Papers
Notes
this example describes the interaction between the system \[\dot{x}(t) = E x(t) + Fu(t)\] with a deadtime – \(x(t)\) is unknown at time \(t\), only the value \(x(t-T)\) is available for some delay \(T>0\) – and a predictor-controller designed to stabilize it (with a finite-spectrum assignment for example). Think of it as an improvement of the classic Smith predictor.↩
MAREVA is the Applied Mathematics Minor of MINES ParisTech “Master’s in Science and Executive Engineering” degree.↩