Nonlinear Systems

This volume is dedicated to nonlinear systems in various fields, and consists of two parts.

This book comprehensively investigates the main principles, core mechanisms, typical problems, and relevant solutions involved in nonlinear systems. This book aims to provide advanced research on nonlinear systems and control schemes for researchers and engineers working in related fields, and thus promote future study in this research area.

The book covers a large class of nonlinear systems with many practical engineering applications. The approach is based on the extension of linear systems theory using the Volterra series. In contrast to the few existing treatments, our approach highlights the algebraic structure underlying such systems and is based on Schwartz’s distributions (rather than functions). The use of distributions leads naturally to the convolution algebras of linear time-invariant systems and the ones suitable for weakly nonlinear systems emerge as simple extensions to higher order distributions, without having to resort to ad hoc operators.

This book focuses on several key aspects of nonlinear systems including dynamic modeling, state estimation, and stability analysis. It is intended to provide a wide range of readers in applied mathematics and various engineering disciplines an excellent survey of recent studies of nonlinear systems.

Symmetries and Semi-invariants in the Analysis of Nonlinear Systems details the analysis of continuous- and discrete-time dynamical systems described by differential and difference equations respectively.

The editors of this book have incorporated contributions from a diverse group of leading researchers in the field of nonlinear systems. To enrich the scope of the content, this book contains a valuable selection of works on fractional differential equations.The book aims to provide an overview of the current knowledge on nonlinear systems and some aspects of fractional calculus.