ON STABILITY AND PROPOSITIONAL FUNCTIONS IN THE THEORY OF GENERALIZED DYNAMICAL SYSTEMS
ON STABILITY AND PROPOSITIONAL FUNCTIONS IN THE THEORY OF GENERALIZED DYNAMICAL SYSTEMS
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Date
1991
Authors
ABDULRAZAQ, ABDULRAHEEM
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Abstract
In this thesis we study some stability concepts for generalized pseudo-dynamical systems under different considerations as well as some semistability of motions and limit sets in semi—systems, and dynamical semi—systems. In chapter one, we give the general introduction to the concept of stability in the theory of generalized dynamical systems In chapter two, starting from stability of sets we present a stability concept for generalized pseudo—dynamical systems. The Lyapunov function and
its bearing on stability is also discussed. Every Lyapunov function must be sufficient for the stability of the set (trajectory or motion) for which it is constructed. In chapter three, we introduce a propositional
function and give a definition of the stability of sets in terms of the propositional function. Based on this we are able to form a link among various types of
stability concepts in the theory of pseudo—dynamical systems. We also touch on the proofs of some theorems which hinge on the construction of Lyapunov functions
for some types of stability and some of their
applications.
Description
A THESIS SUBMITTED TO THE POSTGRADUATE SCHOOL, AHMADU BELLO UNIVERSITY, ZARIA IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF MASTER OF SCIENCE IN MATHEMATICS..
Keywords
STABILITY, PROPOSITIONAL, FUNCTIONS, THEORY, GENERALIZED, DYNAMICAL, SYSTEMS