Harmonic Stability of Power Systems: A Control-Theoretic Definition and Assessment Criteria

What the math gives to ML

The paper provides a transferable stability mechanism for nonlinear systems evolving around nominal periodic trajectories: local harmonic stability is reduced to stability of the linear time-periodic variational system, and the LTP system can be certified with time-invariant LMIs after harmonic state-space lifting. The key neural-network opportunity is to treat periodically varying optimizer updates, cyclic learning-rate schedules, or recurrent inference maps as periodic dynamical systems rather than analyzing them with a single worst-case Jacobian. A periodic Lyapunov certificate can constrain parameter updates or detect instability before loss divergence, while the lifted harmonic representation can diagnose which schedule harmonics amplify perturbations. The most falsifiable prediction is a sharp instability boundary when the monodromy spectral radius crosses one, together with geometric perturbation decay on the stable side.