Quantitative Lyapunov-based stability margins

Derive and validate a rigorous quantitative stability margin from Lyapunov exponents that is analogous to an energy margin or modal damping ratio and is tied to physical instability thresholds.

Background

Most reviewed Lyapunov-exponent methods provide binary stable/unstable decisions or qualitative severity rankings. The paper states that a physically validated continuous margin, comparable to established energy or modal measures, has not yet been established.

References

(5) Stability margin quantification. Current LLE-based methods provide binary stable/unstable decisions or, at best, a qualitative severity ordering. A rigorous, quantitative stability margin (analogous to the energy margin in direct methods or the damping ratio in modal analysis) derived from the LLE and validated against physical instability thresholds remains an open problem.

— Lyapunov Exponents in Power Systems: A Survey of Theory and Applications in Stability, Control, Forecasting, and Protection  (2610.23809 - Almomani et al., 16 Oct 2026) in Section III-K, p. 13

(2) Rigorous probabilistic stability margins. The almost-sure LE theory provides a noise-intensity margin ρ∗. A corresponding margin for nonlinear (not linearized) systems under non-Gaussian, non-stationary renewable disturbances-connecting LLE to formal probabilistic stability guarantees-is absent.

— Lyapunov Exponents in Power Systems: A Survey of Theory and Applications in Stability, Control, Forecasting, and Protection  (2610.23809 - Almomani et al., 16 Oct 2026) in Section VII-H, p. 29