The primary goal of this paper is to describe the classes of all polynomial vector fields such that the associated dynamical system admits some polynomial Lyapunov function v(x). By fixing or constraining the time derivative of v(x) in different ways, several different cases are studied. Hints are given about how to use the results for stability analysis and for non-polynomial systems.
Menini, L., Tornambe', A. (2014). On a Lyapunov equation for polynomial continuous-time systems. INTERNATIONAL JOURNAL OF CONTROL, 87(2), 393-403 [10.1080/00207179.2013.835869].
On a Lyapunov equation for polynomial continuous-time systems
MENINI, LAURA;TORNAMBE', ANTONIO
2014-01-01
Abstract
The primary goal of this paper is to describe the classes of all polynomial vector fields such that the associated dynamical system admits some polynomial Lyapunov function v(x). By fixing or constraining the time derivative of v(x) in different ways, several different cases are studied. Hints are given about how to use the results for stability analysis and for non-polynomial systems.File in questo prodotto:
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