Posers and Puzzles

Posers and Puzzles

  1. In Christ
    Joined
    30 Apr '07
    Moves
    172
    25 May '11 02:16
    So there's a feedback connection between G(s) = 1/(1 + s)^2 and a nonlinear function/map psi(t, y) = a*y*sin(w*t). How can I use the small gain theorem to find conditions on "a" so that this connection is finite gain L-infinity stable?

    I'm pretty sure I need to use the peak-to-peak gain of G(s), but I'm not sure how to find its impulse response, or what to do about getting the infinity norm of psi.
  2. Standard memberPalynka
    Upward Spiral
    Halfway
    Joined
    02 Aug '04
    Moves
    8702
    25 May '11 12:35
    I'm not sure I understand the feedback. s is the input and y is the output? If so, do is it like:

    s -> G(s) -> y
    ....| ........ |
    .....psi(y,t)
  3. In Christ
    Joined
    30 Apr '07
    Moves
    172
    25 May '11 12:59
    Exactly.