Regular Elements and Global Controllability in SL(d, R)

  • Authors:

  • Richard M. Mamani Troncoso

  • Affiliations:

  • Departamento de Matemáticas y Estadística, Universidad Nacional San Agustin de Arequipa, UNSA-Perú

  • Venue:
  • Journal of Dynamical and Control Systems
  • Year:
  • 2004

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Abstract

We introduce a generalized concept of split-regular elements and study the dynamics of such elements on the flag manifolds corresponding to the Lie group SL(d, R). Based on these concepts, we obtain the stable and unstable manifolds, the Morse decomposition, and obtain the limit sets inside the corresponding control sets. These dynamical aspects are studied with the purpose of applying them in order to extend a result of global controllability of discrete-time bilinear systems defined by elements of sl(d, R).