Year: 2026
Type: preprint
Abstract: Approximating the maximum retained energy fraction in globally asymptotically stable quadratic systems of growing dimension is NP-hard at every fixed positive additive error below $1/2$, even when strict quartic Lyapunov functions and strictness proofs are constructed in polynomial time and included in the input. Polynomial-factor approximation is also NP-hard for the least dissipated fraction, energy-halving time and structured coefficient distance to loss of asymptotic stability. For a partially damped family, minimum unit-sphere coupling norm equals that distance, with two-sided inverse-square halving-time bounds at distances in $(0,1/2]$ and explicit coefficient factors. Additive hardness persists under structured coefficient perturbations and direct damping, even with global exponential stability, a strict quadratic Lyapunov function and a Hurwitz Jacobian.
Source: arXiv (Cornell University)
Author: Bhattacharjee, Subhransu S.
Institution: Australian National University
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223226939