Cone-Valued Lyapunov Functions
Abstract
**Please note that the full text is embargoed** ABSTRACT: It is very well known that employing a single
Lyapunov function and the theory of scalar
differential inequality offers a useful
mechanism to study a variety of qualitative
problems of differential equations in a unified
way [10]. Nevertheless, when using this
powerful technique for concrete problems, the
main difficulty we face is the lack of general
method of constructing a Lyapunov function.
This naturally beads to the development of the
method of vector Lyapunov functions which
utilizes several Lyapunov-like functions and
the theory of vector differential inequalities
in a fruitful manner [5,8-12]. This method
offers a more flexible mechanism to discuss
qualitative properties of nonlinear systems.
Also, it provides an effective tool to
investigate the properties of large scale
interconnected dynamical and control systems
whose multivariability, composite structure,
multi-connection and the variety of the nature
of subsystems make the construction of a single
Lyapunov function much more difficult.
Moreover, several Lyapunov functions result in
a natural way in the study of such systems by
the decomposition and aggregation method
[1,3,5,6,13-15].