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Tools for Analysis of Dynamic Systems: Lyapunov s Methods

1 Tools for Analysis of Dynamic Systems: Lyapunov s Methods Stanis aw H. ak School of Electrical and Computer Engineering ECE 680 Fall 2013 2 A. M. Lyapunov s (1857--1918) Thesis 3 Lyapunov s Thesis 4 Lyapunov s Thesis Translated 5 Some Details About Translation 6 Outline Notation using simple examples of dynamical system models Objective of Analysis of a nonlinear system Equilibrium points Lyapunov functions Stability Barbalat s lemma 7 A Spring-Mass Mechanical system x---displacement of the mass from the rest position 8 Modeling the Mass-Spring system Assume a linear mass, where k is the linear spring constant Apply Newton s law to obtain Define state variables.

Objectives of Analysis of Nonlinear Systems Similar to the objectives pursued when investigating complex linear systems Not interested in detailed solutions, rather one seeks to characterize the system behavior---equilibrium points and their stability properties A device needed for nonlinear system analysis summarizing the system

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