Lyapunov Stability Analysis of the Moog Ladder Filter and Dissipativity Aspects in Numerical Solutions

Thomas Hélie
DAFx-2011 - Paris
This paper investigates the passivity of the Moog Ladder Filter and its simulation. First, the linearized system is analyzed. Results based on the energy stored in the capacitors lead to a stability domain which is available for time-varying control parameters meanwhile it is sub-optimal for time-invariant ones. A second storage function is proposed, from which the largest stability domain is recovered for a time-invariant Q-parameter. Sufficient conditions for stability are given. Second, the study is adapted to the nonlinear case by introducing a third storage function. Then, a simulation based on the standard bilinear transform is derived and the dissipativity of this numerical version is examined. Simulations show that passivity is not unconditionally guaranteed, but mostly fulfilled, and that typical behaviours of the Moog filter, including self-oscillations, are properly reproduced.