Identifier
etd-07112005-185010
Degree
Doctor of Philosophy (PhD)
Department
Mathematics
Document Type
Dissertation
Abstract
A dynamical polysystem consists of a family of continuous dynamical systems, all acting on a given metric space. The first chapter of the present thesis shows a generalization of control systems via dynamical polysystems and establishes the equivalence of the two notions under certain lipschitz condition on the function defining the dynamics. The remaining chapters are focused on a basic theory of dynamical polysystems. Some topological properties of limit sets are described in Chapter 2. Chapters 3 and 4 provide characterizations for various notions of strong stability. Chapter 5 makes use of the theory of closed relations to study Lyapunov functions. Prolongations and absolute stability make the object of the last chapter.
Date
2005
Document Availability at the Time of Submission
Release the entire work immediately for access worldwide.
Recommended Citation
Cazacu, George, "Stability in dynamical polysystems" (2005). LSU Doctoral Dissertations. 101.
https://repository.lsu.edu/gradschool_dissertations/101
Committee Chair
Jimmie Lawson
DOI
10.31390/gradschool_dissertations.101