Global Stability of a Class of Difference Equations on Solvable Lie Algebras

Autor:	McCarthy, Philip James, Nielsen, Christopher
Rok vydání:	2019
Předmět:	Mathematics - Dynamical Systems 17B30 17B80 39A30 93D05 93D20
Druh dokumentu:	Working Paper
Popis:	Motivated by the ubiquitous sampled-data setup in applied control, we examine the stability of a class of difference equations that arises by sampling a right- or left-invariant flow on a matrix Lie group. The map defining such a difference equation has three key properties that facilitate our analysis: 1) its power series expansion enjoys a type of strong convergence; 2) the origin is an equilibrium; 3) the algebraic ideals enumerated in the lower central series of the Lie algebra are dynamically invariant. We show that certain global stability properties are implied by stability of the Jacobian linearization of dynamics at the origin. In particular global asymptotic stability. If the Lie algebra is nilpotent, then the origin enjoys semiglobal exponential stability.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1902.01489 Zobrazit plný text záznamu View this record from Arxiv