Performance analysis of modern communication systems has lead to a revision and sharpening of nonlinear stability analysis techniques developed over the last century. Applicability of such techniques involves a number of areas, including process control systems, active queue management in data networks, and other branches of engineering. This monograph presents some recent performance analysis results within a unified stability analysis framework. Several interesting counter-examples to the existing nonlinear stability theory are given. Additionally, several cutting-edge case studies from air traffic control systems and data networks are presented to further illustrate the applications of the theory. The main theoretical results build upon the well-established multiplier theory, which has received much interest because of recent advances in software packages such as the Linear Matrix Inequality (LMI) toolbox. "Qualitative Nonlinear Dynamics of Communication Networks" is a useful reference for graduate students, and practitioners in control, computer, electrical, aerospace, and mechanical engineering.
It may be used as a supplementary text for nonlinear stability courses at the graduate level. Prerequisites are a familiarity with elementary control theory, linear systems theory, matrix theory, and functional analysis.
Glossary.- List of Tables.- List of Figures.- Table of Notation.- Preface.- Introduction.- Extension of Zames-Falb Multipliers for MIMO Nonlinearities.- Multipliers for Special Classes of MIMO Nonlinearities.- Incremental Positivity Preservation Properties of Multipliers.- Case Study I: Air Traffic Control Systems.- Case Study II: Scalability of Communication Protocols.- Case Study III: Active Queue Management.- Bibliography.- Appendices.- Index