Characterization of the stability region of the nonlinear discrete dynamical systems

Author(s)

Elaine Santos Dias

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Escola de Engenharia de São Carlos (EESC/SBD)
• Defense date: 2016-09-30

Examining board members

Luís Fernando Costa Alberto; Grace Silva Deaecto; Márcio Fuzeto Gameiro

• Advisor: Luís Fernando Costa Alberto

Abstract

The study of the stability region is very important in the sciences, engineering applications, and in nonlinear control systems. In this work, a complete characterization for both the stability region and the stability boundary of stable xed points of a nonlinear discrete dynamical systems is developed. The results of this work extend the characterization of the stability region already proposed in the literature for a larger class of systems, which are modeled by dieomorphisms and which admit the presence of periodic orbits and xed points on the stability boundary. Several dynamical and topological characterizations are proposed to the stability boundary. Moreover, several necessary and sucient conditions for xed points and periodic orbits to lie on the stability boundary are derived. Numerical examples, including the model of a symmetric neural network with 2-neurons, illustrate the results proposed in this work. (AU)

• FAPESP's process: 14/14141-8 - Study of the stability region of discrete dynamical systems
• Grantee: Elaine Santos Dias
• Support Opportunities: Scholarships in Brazil - Master