EEEN50100 Stability Analysis of Nonlinear Systems

Academic Year 2023/2024

The objective of this module is to show the students basic concepts of stability of nonlinear dynamical systems and maps. In particular, the main concepts of bifurcation theory and Lyapunov stability criteria will be provided. The approach is both theoretical and practical. Each topic is first formulated in mathematical terms and suitable numerical methods are discussed. Several examples, mostly based on major power systems blackouts, as well as control remedial actions are described. The students will also get familiar with open source software to solve stability analysis of nonlinear dynamical systems.

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Curricular information is subject to change

Learning Outcomes:

Concepts of stability analysis of nonlinear dynamical systems. Concepts of bifurcation theory. Lyapunov stability first and second criteria. Numerical techniques for the stability analysis of nonlinear differential equations. Basic concepts of delay differential equations. Basic concepts of chaos. Real-world examples based on power systems blackouts.

Indicative Module Content:

Definitions of nonlinear system stability. Basic bifurcation theory concepts. Stability of maps. Small-signal stability analysis (Lyapunov first stability criterion). Transient Stability analysis and transient energy function (Lyapunov second stability criterion). Voltage stability. Frequency stability. Monodromy matrix and Floquet multipliers. Routes to chaos.

Student Effort Hours: 
Student Effort Type Hours
Autonomous Student Learning










Approaches to Teaching and Learning:
Lectures with a blend of theory, numerical examples and practical applications. 
Requirements, Exclusions and Recommendations

Not applicable to this module.

Module Requisites and Incompatibles
EEEN40010 - Control Theory

Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Assignment: Short report or review (15-20 pages) on a topic agreed with the module supervisor Unspecified n/a Graded Yes


Carry forward of passed components
Remediation Type Remediation Timing
In-Module Resit Prior to relevant Programme Exam Board
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Feedback individually to students, post-assessment

How will my Feedback be Delivered?

Not yet recorded.

Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.

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