loriapanteley2004cascade

Cascaded Nonlinear Time-Varying Systems: Analysis and Design

Authors: Antonio Loría, Elena Panteley · Year: 2005 · Venue: Ch. 2 (pp. 23–64) of Advanced Topics in Control Systems Theory: Lecture Notes from FAP 2004 (LNCIS 311), Springer · Raw: md (full volume; chapter at line ~3184) · pdf

Summary

A lecture-notes chapter on the Lyapunov stability of nonlinear time-varying (NLTV) cascaded systems — systems in “open loop” where a driving subsystem ${\Sigma }_2$ feeds a driven subsystem ${\Sigma }_1$. It states the analysis problem (when is the cascade UGAS?) and the design problem (build a closed loop with cascade structure), collects the main growth-rate / boundedness conditions, and gives control-design applications. In this corpus it is the provenance for the R4 cascade layer, the companion to panteley2001growth.

Key Claims

• Cascade UGAS conditions. With ${\Sigma }_1$ UGAS (and ISS-like in the interconnection input) and ${\Sigma }_2$ UGAS, the cascade is UGAS provided solutions are bounded — boundedness supplied by a growth-rate condition on the interconnection term.
• Analysis vs design split. Part 2 is pure stability analysis (no control design); Part 3 shows cases where deliberately shaping a closed loop into cascade form beats a monolithic backstepping Lyapunov design.
• Time-varying emphasis. Results target the non-autonomous case relevant to trajectory tracking, where LaSalle-type invariance does not apply.

Method

Lecture-notes synthesis of published results (proofs referenced, not reproduced): Lyapunov / ISS conditions, growth-rate bounds on the interconnection, and worked control-design examples.

Regime note. General NLTV systems theory — no manipulator/spacecraft model — so the free-flying vs free-floating axis does not apply; a tool text feeding the tracking cascades.

Relevance to thesis

The free-flying manipulator’s tracking controller is analyzed as a cascade (a converged inner loop driving the outer error); R4’s charter cites this chapter for the UGAS-of-cascades conditions. This page supplies the resolving bibkey.

Connections

Topics: cascaded systems · trajectory tracking · input to state stability · Lyapunov stability Sources: panteley2001growth · panteley1998global

Key Equations / Quotes

Chapter scope, verbatim from the corpus text layer (modern LaTeX; symbols preserved, only cosmetic ligature noise):

“The general topic of study is Lyapunov stability of nonlinear time-varying cascaded systems. Roughly speaking these are systems in ‘open loop’ as illustrated in the figure below.”

Open Questions

• The corpus PDF/md is the entire edited volume (115 pp), not just this chapter; the Loría–Panteley cascade chapter begins at raw md line ~3184 (printed pp. 23–64). Other chapters (e.g. Karagiannis–Ortega–Astolfi I&I, Ch. 1) share the file.
• bibkey note: the key retains the ctrllib-assigned loriapanteley2004cascade (two surnames; “2004” = the FAP 2004 school), while the .bib year is the printed publication year 2005. This is a deliberate, documented mismatch — the research-wiki lint emits two soft warnings (bibkey surname vs first-author; bibkey year vs .bib year). Rename to loria2005cascade to clear them if preferred.