ECE 5220 - [Nonlinear Systems]

Spring (not offered every year). 3 credits. Letter grades only.

Prerequisite: ECE 2200.

H. D. Chiang.

Introduction to nonlinear systems, four notions of steady state behavior of nonlinear systems, concepts of nonlinear stability and asymptotical stability, stability/instability of steady states, Lyapunov function theorems and tools, construction of Lyapunov functions, system analysis based on Lyapunov function theorems. Concepts of degree of stability or robustness of stability. Introduction of stability regions. Dynamic and geometric properties of stability regions. Characterization of stability regions and comprehensive schemes for estimating stability regions of large-scale nonlinear systems. This course will focus on applications of stability regions to the design of associative memory in artificial neural networks, to advanced solution methods for nonlinear optimization problems, and to optimal training of artificial neural networks.