Synopses & Reviews
Linear, Time-varying Approximations to Nonlinear Dynamical Systems introduces a new technique for analysing and controlling nonlinear systems. This method is general and requires only very mild conditions on the system nonlinearities, setting it apart from other techniques such as those - well-known - based on differential geometry. The authors cover many aspects of nonlinear systems including stability theory, control design and extensions to distributed parameter systems. Many of the classical and modern control design methods which can be applied to linear, time-varying systems can be extended to nonlinear systems by this technique. The implementation of the control is therefore simple and can be done with well-established classical methods. Many aspects of nonlinear systems, such as spectral theory which is important for the generalisation of frequency domain methods, can be approached by this method.
Review
From the reviews: "The present book is a research monograph written in the style of a graduate text in the broad subject of linear time-varying approximations to nonlinear dynamical systems. ... The book is a self-contained presentation of essential results with rigorous proofs. It is well written with care and a lot of interest. I strongly recommend the book to graduate students and mathematicians as well as engineers." (Themistocles M. Rassias, Mathematical Reviews, Issue 2011 g)
Synopsis
A new technique for analysing and controlling nonlinear systems is introduced in this book. Although the methods outlined are novel, they can be simply implemented using pre-existing and widely known classical control ideas.
Table of Contents
Introduction.- Basic Approximation Theory.- Linear, Time-varying Systems.- General Spectral Theory of Nonlinear Systems.- Spectral Assignment in Linear, Time-varying Systems.- Optimal Control of Nonlinear Systems.- Application to Nonlinear Sliding-mode Control.- Connection with Fixed-point Theory and Existence of Periodic Solutions.- Generalisations to Partial Differential Equations.- Summary, Conclusions and Prospects for Development.- Appendices.