Controllability and semigroups of invariant control systems on Sl (n, H)

Author(s)

Rodrigues, Bruno A. ; San Martin, Luiz A. B. ; Santana, Alexandre J.

• Document type: Journal article
• Source: Mathematics of Control, Signals, and Systems (MCSS); v. 34, n. 2, p. 12-pg., 2022-02-11.

Abstract

Let Sl (n, H) be the Lie group of n x n quaternionic matrices g with vertical bar det g vertical bar = 1. We prove that a subsemigroup S subset of Sl (n, H) with nonempty interior is equal to Sl (n, H) if S contains a special subgroup isomorphic to Sl (2, H). From this, we give sufficient conditions on A, B is an element of sl (n, H) to ensure that the invariant control system (g)over dot = Ag + uBg is controllable on Sl (n, H). We prove also that these conditions are generic in the sense that we obtain an open and dense set of controllable pairs (A, B) is an element of sl (n, H)(2). (AU)

• FAPESP's process: 18/13481-0 - Geometry of control, dynamical and stochastic systems
• Grantee: Marco Antônio Teixeira
• Support Opportunities: Research Projects - Thematic Grants