slotine1991applied

Applied Nonlinear Control

Authors: Jean-Jacques E. Slotine, Weiping Li · Year: 1991 · Venue: Prentice Hall, Englewood Cliffs, NJ Raw: md (full book) · pdf

Summary

A design-oriented graduate text on nonlinear control, in two parts: analysis (phase-plane, Lyapunov theory, advanced/non-autonomous stability, describing functions) and design (feedback linearization, sliding control, adaptive control, control of multi-input physical systems). The full book is OCR’d into the corpus. Its role in this project is as the canonical cite for Barbalat’s lemma and its Lyapunov-like corollary — the tool for concluding convergence of a rate $\dot{V}$ in non-autonomous closed loops, where LaSalle’s invariance principle does not apply.

Key Claims

• Barbalat’s lemma (§4.5.2, Lemma 4.2). If a differentiable $f(t)$ has a finite limit as $t\to \infty$ and $\dot{f}$ is uniformly continuous, then $\dot{f}(t)\to 0$. Uniform continuity is the extra hypothesis that turns “energy settles” into “the rate dies out.”
• Lyapunov-like lemma (§4.5.2, Lemma 4.3). If a scalar $V(x,t)$ is lower bounded, has $\dot{V}\le 0$ (negative semi-definite), and $\dot{V}$ is uniformly continuous, then $\dot{V}(t)\to 0$. This is the form used in adaptive/tracking stability proofs (Slotine’s Example 4.13 stresses: gives $\dot{V}\to 0$, not state convergence).
• Sliding control (Ch. 7) and adaptive control (Ch. 8) give constructive Lyapunov-based designs for uncertain and time-varying plants; feedback linearization (Ch. 6) cancels nonlinearities via coordinate/feedback transformation.

Method

Textbook: theory paired with worked control-design examples, oriented toward robot manipulators and Euler–Lagrange systems (the motivating application class for the tracking cascades this project studies).

Regime note. General nonlinear-control text — no spacecraft or base-actuation model — so the free-flying vs free-floating distinction does not arise; it is a tool text.

Relevance to thesis

Barbalat’s lemma and its Lyapunov-like corollary (§4.5) are formalized as a sealed Lean module (Barbalat.lean) and are the workhorse behind the non-autonomous convergence rungs — the free-flying manipulator’s closed-loop tracking-error dynamics are non-autonomous, so LaSalle does not apply and Barbalat is the correct substitute. This page supplies the resolving bibkey so those derivations cite the text rather than a plain-text mention.

Connections

Topics: Lyapunov Stability · Trajectory Tracking · Sliding Mode Control · Feedback Linearization Sources: khalil2002nonlinear · khalil1996nonlinear · panteley2001growth

Key Equations / Quotes

Barbalat’s lemma (Lemma 4.2), read verbatim off the corpus OCR:

“If the differentiable function $f(t)$ has a finite limit as $t\to \infty$, and if $\dot{f}$ is uniformly continuous, then $\dot{f}(t)\to 0$ as $t\to \infty$.”

Lyapunov-like lemma (Lemma 4.3):

“If a scalar function $V(x,t)$ satisfies the following conditions: $V(x,t)$ is lower bounded; $\dot{V}(x,t)$ is negative semi-definite; $\dot{V}(x,t)$ is uniformly continuous in time, then $\dot{V}(x,t)\to 0$ as $t\to \infty$.”

Open Questions

• ISBN was not present in the OCR’d front matter (image-only title page), so it is omitted from the .bib entry rather than guessed — fill in if a clean scan surfaces.