Absolute stability of nonlinear control systems
The concept of absolute stability of nonlinear and time-varying systems has a history of forty years, however, as the author of the present book states, most of the available work is concerned with sufficient conditions of absolute stability while there is a lack of necessary and sufficient conditions. The main purpose of this book is to present the latest results of the author and some others on developments in this important field. The aim of the book is twofold: theoretically, to give as many as possible necessary and sufficient conditions of absolute stability of various nonlinear control systems; in applications, to derive simple enough and constructive algebraic sufficient conditions from these theoretical results for use in practical work. Modern methods and tools such as M-matrices, K-class functions, Dini-derivatives, partial stability, and set stability are extensively used. The book is subdivided in 6 chapters. It covers non-autonomous and discrete control systems, systems with several nonlinear control terms and systems described by functional differential equations. The book provides a wealth of methods and ideas and is valuable to everyone who is interested in nonlinear control theory and its applications.
scientific article; zbMATH DE number 700085