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Formalize both branches of Lyapunov's indirect method - #15

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AnandGokhale merged 3 commits into
AnandGokhale:mainfrom
math-experiments:codex/issue-9-lyapunov-indirect-method
Sep 22, 2026
Merged

AnandGokhale merged 3 commits into
AnandGokhale:mainfrom
math-experiments:codex/issue-9-lyapunov-indirect-method

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@math-experiments

@math-experiments math-experiments commented Sep 10, 2026

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Closes #9.

Summary

  • Add axiom-free Hurwitz, matrix-exponential, Fréchet-remainder, quadratic-form, and arbitrary-Q Lyapunov-equation infrastructure.
  • Prove that a Hurwitz Jacobian gives finite-forward local exponential stability, with compatibility corollaries for the legacy API.
  • Prove that a positive-real complex eigenpair gives forward instability via a real Hermitian quadratic certificate and generic Chetaev machinery.
  • Update umbrella imports, README, roadmap, and blueprint.

The primary results quantify over finite forward solution segments, avoiding finite-escape vacuity. The stable theorem does not itself package forward-complete existence.

Checks

  • lake build
  • lake exe runLinter --no-build
  • lake exe mk_all --check
  • lake build :blueprint
  • leanblueprint checkdecls
  • lake build LeanForControl:docs
  • git diff --check

@AnandGokhale

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Superseded by #17, which has been merged. This branch predated a subsequent directory reorg on main and could not be merged as-is (conflicts in LeanForControl.lean, README.md, blueprint/src/content.tex, Stability/plan.md, plus a dependency on a complexification helper that main's independent Hurwitz rewrite had dropped). #17 relocates this work into Stability/LyapunovIndirect/, fixes the conflicts and the dependency gap, and is now on main. Closing this one.

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Prove the indirect method of Lyapunov (linearization)

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