Some conditions of regularity of linear extensions of dynamical systems with respect to selected variables

Abstract

In this paper, we dealt with the issue of the regularity of the linear extension of the dynamical system. Using the Lyapunov function with the changeable sign, conditions for the regularity of the entire examined dynamical system were given, assuming that only a certain separate part of this system was regular. Our results were generalized and improved to the wider class of dynamical systems, for which only a certain combination of components is regular.

Keywords

• Green's function
• linear extension of dynamical systems
• linear regular extensions
• weak regularity
• quadratic form
• Lyapunov's function