Lyapunov Function for the Nonlinear Moog Voltage Controlled Filter
Stefan Bilbao
TL;DR
This paper introduces a novel Lyapunov function for the nonlinear Moog voltage-controlled filter, enabling stability analysis across all parameter ranges and supporting Hamiltonian-based numerical simulations.
Contribution
A new Lyapunov function is proposed for the nonlinear Moog VCF, providing comprehensive stability proof and a foundation for advanced simulation methods.
Findings
Proves stability over entire parameter range
Supports Hamiltonian-based numerical simulation
Applicable under zero-input and nonlinear autonomous conditions
Abstract
In this short report, a new Lyapunov function for the Moog voltage-controlled filter is demonstrated, under zero-input conditions, and under nonlinear autonomous conditions (i.e. when parameters are not time-varying). The new definition allows for a proof of stability over the entire allowable range of parameters (cutoff frequency and resonance), and can be used as a starting point for Hamiltonian-based numerical simulation methods.
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Taxonomy
TopicsNonlinear Dynamics and Pattern Formation · Control and Stability of Dynamical Systems · Model Reduction and Neural Networks