BIBO Stability of Linear Control Systems on Lie Group Examples

Ayala V.; Torreblanca Todco M.L.; Valdivia Hanco W.E. · Mathematics (2026) · DOI: 10.3390/math14122141

Resumen

We develop a collection of nontrivial examples that illustrate and test recent stability results for linear control systems ( (Formula presented.) ) on Lie groups. We treat the main structural classes: Abelian ( (Formula presented.) ), nilpotent (Heisenberg), solvable non-nilpotent (rigid motions of the plane (Formula presented.) ), compact semisimple ( (Formula presented.) ), noncompact semisimple ( (Formula presented.) via Iwasawa decomposition) and mixed/Levi-type groups. The examples are designed to (i) show the sharpness of geometric boundedness criteria, (ii) exhibit typical failure modes (exponential escape, polynomial central drift, noncompact neutrals), and (iii) demonstrate how the canonical quotient and suitable outputs recover (Formula presented.) stability. The executive framework ( (Formula presented.) existence/uniqueness, canonical quotient (Formula presented.), (Formula presented.) characterization, robustness and ISS-type bounds) is briefly recalled; the main part of the paper consists of detailed worked examples implementing the practical checklist for applying these theorems.

Instituciones: Universidad Nacional de San Agustín de Arequipa