On homogeneous density functions. (English) Zbl 1043.93057
Rantzer, Anders (ed.) et al., Directions in mathematical systems theory and optimization. Berlin: Springer (ISBN 3-540-00065-8/pbk). Lect. Notes Control Inf. Sci. 286, 261-274 (2003).
The paper deals with the system
\[
\begin{gathered} \dot x = f(x),\quad x\in \mathbb{R}^n,\\ f\in C^1(\mathbb{R}^n,\mathbb{R}^n),\quad f(0) = 0. \end{gathered}\tag{1}
\]
For system (1) the authors consider homogeneous density functions for proving global attractivity of the zero equilibrium in a homogeneous system. It is shown that the existence of such a function is guaranteed when the equilibrium is asymptotically stable or, in the more general case, when there exists a nonhomogeneous density function for the same system satisfying some reasonable conditions.
For the entire collection see [Zbl 1005.00024].
For the entire collection see [Zbl 1005.00024].
Reviewer: Anatoly Martynyuk (Kyïv)
MSC:
93D20 | Asymptotic stability in control theory |
93C10 | Nonlinear systems in control theory |
93D09 | Robust stability |