Article Contents
Article Contents

# Topological conjugacy for affine-linear flows and control systems

• Hyperbolic affine-linear flows on vector bundles possess unique bounded solutions on the real line. Hence they are topologically skew conjugate to their linear parts. This is used to show a classification of inhomogeneous bilinear control systems.
Mathematics Subject Classification: Primary: 37B55, 37N35; Secondary: 93B10.

 Citation:

•  [1] A. A. Agrachev and Y. L. Sachkov, "Control Theory from a Geometric Viewpoint," Springer-Verlag, New York, 2004. [2] B. Aulbach and T. Wanner, Integral manifolds for Carathéodory type differential equations in Banach spaces, in "Six Lectures on Dynamical Systems" (eds. B. Aulbach and F. Colonius), World Scientific, (1996), 45-119. [3] V. Ayala, F. Colonius and W. Kliemann, On topological equivalence of linear flows with applications to bilinear control systems, J. Dynamical and Control Systems, 13 (2007), 337-362.doi: doi:10.1007/s10883-007-9021-9. [4] L. Baratchart, M. Chyba and J.-P. Pomet, A Grobman-Hartman theorem for control systems, J. Dynamics and Differential Equations, 19 (2007), 95-107. [5] F. Colonius and W. Kliemann, "The Dynamics of Control," Birkhäuser, Boston, 2000. [6] Nguyen Dinh Cong, "Topological Dynamics of Random Dynamical Systems," Oxford Math. Monogr., Clarendon Press 1997. [7] D. L. Elliott, "Bilinear Control Systems. Matrices in Action," Applied Mathematical Sciences, 169 Springer-Verlag, New York, 2009. [8] C. Robinson, "Dynamical Systems. Stability, Symbolic Dynamics, and Chaos," CRC Press, 1999.

• on this site

/