dc.description.abstract | **Please note that the full text is embargoed** ABSTRACT: The notion of "practical stability" was discussed in the monograph by LaSalle and Lefschetz [6] in which they point out that stability investigations
may not assure "practical stability" and vice versa. For example an aircraft may oscillate around a mathematically unstable path, yet its performance
may be acceptable. Motivated by this, Weiss and Infante introduced the concept of finite time stability [7]. They were interested in the behavior of
systems contained within specified bounds during a fixed time interval. Many problems fall into this category including the travel of a space vehicle
between two points and the problem, in a chemical process, of keeping the temperature within certain bounds.
In particular, Weiss and Infante [7] provided sufficient conditions for finite time stability in terms of Lyapunov functions. Moreover, Weiss [9]
provided necessary and sufficient conditions for uniform finite time stability and exponential contractive stability. These results were extended
by Kayande [3] who obtained necessary and sufficient conditions for contractive stability (without requiring the exponential behavior assumed in [9]).
The sufficiency part of the above results were extended by Kayande and Wong [4], and Gunderson [1], who applied the comparison principle. Moreover
Hallam and Komkov [2] generalized the concept of the finite time stability of the zero solution to that of arbitrary closed sets. | en |