Nonlinear Systems Stability Analysis: Lyapunov-Based Approach, 1st Edition (Paperback) book cover

Nonlinear Systems Stability Analysis

Lyapunov-Based Approach, 1st Edition

By Seyed Kamaleddin Yadavar Nikravesh

CRC Press

319 pages | 40 B/W Illus.

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The equations used to describe dynamic properties of physical systems are often nonlinear, and it is rarely possible to find their solutions. Although numerical solutions are impractical and graphical techniques are not useful for many types of systems, there are different theorems and methods that are useful regarding qualitative properties of nonlinear systems and their solutions—system stability being the most crucial property. Without stability, a system will not have value.

Nonlinear Systems Stability Analysis: Lyapunov-Based Approachintroduces advanced tools for stability analysis of nonlinear systems. It presents the most recent progress in stability analysis and provides a complete review of the dynamic systems stability analysis methods using Lyapunov approaches. The author discusses standard stability techniques, highlighting their shortcomings, and also describes recent developments in stability analysis that can improve applicability of the standard methods. The text covers mostly new topics such as stability of homogonous nonlinear systems and higher order Lyapunov functions derivatives for stability analysis. It also addresses special classes of nonlinear systems including time-delayed and fuzzy systems.

Presenting new methods, this book provides a nearly complete set of methods for constructing Lyapunov functions in both autonomous and nonautonomous systems, touching on new topics that open up novel research possibilities. Gathering a body of research into one volume, this text offers information to help engineers design stable systems using practice-oriented methods and can be used for graduate courses in a range of engineering disciplines.

Table of Contents

Basic Concepts

Mathematical Model for Nonlinear Systems

Existence and Uniqueness of Solutions

Qualitative Behavior of Second-Order Linear Time-Invariant Systems

Stability Analysis of Autonomous Systems

System Preliminaries

Lyapunov’s Second Method for Autonomous Systems

Lyapunov Function Generation for Linear Systems

Lyapunov Function Generation for Nonlinear Autonomous Systems

Relaxed Lyapunov Stability Conditions

New Stability Theorems

Lyapunov Stability Analysis of a Transformed Nonlinear System


Stability Analysis of Nonautonomous Systems


Relaxed Lyapunov Stability Conditions

New Stability Theorems

Application of Partial Stability Theory in Nonlinear Nonautonomous System Stability Analysis

Stability Analysis of Time-Delayed Systems


Stability Analysis of Linear Time-Delayed Systems

Delay-Dependent Stability Analysis of Nonlinear Time-Delayed Systems

An Introduction to Stability Analysis of Linguistic Fuzzy Dynamic Systems

TSK Fuzzy Model System’s Stability Analysis

Linguistic Fuzzy Stability Analysis Using a Fuzzy Petri Net

Linguistic Model Stability Analysis

Stability Analysis of Fuzzy Relational Dynamic Systems

Asymptotic Stability in a Sum-Prod FRDS

Asymptotic Convergence to the Equilibrium State

About the Author

Seyyed Kamaleddin Yadavar Nikravesh, Ph.D., is a professor in the electrical engineering department at Amirkabir University of Technology. His research interests include dynamic and biomedical modeling, system stability, and system optimization. He has published five different books on electrical circuit analysis, optimal control systems, industrial control system analysis, industrial control system synthesis and design, and system stability analysis: Lyapounov-based approach. He has also published more than 180 journal and conference papers, mostly in systems modeling, and system stability analysis and synthesis, which form the main structure of his present book.

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Chemistry / Industrial & Technical