khalil1996nonlinear

Nonlinear Systems (2nd edition)

Authors: Hassan K. Khalil · Year: 1996 · Venue: Prentice Hall, Upper Saddle River, NJ (2nd ed.)

Bib-only source (no corpus markdown yet)

This edition has no OCR in the corpus — Docs/raw/md/khalil1996nonlinear/ is empty and there is no raw/pdf/ for it. The bibkey exists so the Lean stability pages can cite it by a resolving key; the concepts are cited by name pending OCR. Do not conflate with the 3rd ed. (khalil2002nonlinear) — chapter numbering differs between editions, so cite by edition.

Summary

The 2nd edition of Khalil’s nonlinear-control text (13 chapters). Cited across the Lean stability library as the standard reference for the comparison lemma, ultimate boundedness, finite escape time, class-𝒦 comparison functions, and the Rayleigh-quadratic Lyapunov bound ${\lambda }_{\min }(P)\Vert x{\Vert }^2\le x^{\top }Px\le {\lambda }_{\max }(P)\Vert x{\Vert }^2$.

Key Claims

Cited by name (precise sections deferred until the 2nd-ed OCR lands — flagged, not fabricated):

• Comparison lemma and class-𝒦/𝒦ℒ comparison functions — the substrate for uniform stability of non-autonomous systems.
• Ultimate boundedness and finite escape time — the vocabulary the time-varying comparison rung uses.
• Standard Lyapunov-candidate properties (positive definite, radially unbounded / coercive) used in the block-Lyapunov argument.

Method

Graduate textbook; theorems with proofs and worked examples. (Not yet read from the corpus — bib-only.)

Regime note. General nonlinear-systems reference; the free-flying vs free-floating distinction does not arise.

Relevance to thesis

Referenced in the sources: frontmatter of the Lean modules rayleigh_sandwich, block_lyapunov, lyapunov_comparison, and time_varying_comparison. Those pages currently note “khalil1996nonlinear (no wiki page yet)”; this page resolves that. Where a precise section is needed (e.g. comparison functions §4.4 Def. 4.2–4.3), the derivations pin the 3rd ed. (khalil2002nonlinear), whose relevant block is in the corpus.

Connections

Topics: Lyapunov Stability · Input to State Stability Sources: khalil2002nonlinear (3rd ed.) · slotine1991applied

Open Questions

• 2nd-ed OCR pending (Ch. 3–9 flagged in the .bib note). Until then, section numbers are cited by name only.