Input-to-State Stability
Description
Input-to-State Stability presents the dominating stability paradigm in nonlinear control theory that revolutionized our view on stabilization of nonlinear systems, design of robust nonlinear observers, and stability of nonlinear interconnected control systems.
The applications of input-to-state stability (ISS) are manifold and include mechatronics, aerospace engineering, and systems biology. Although the book concentrates on the ISS theory of finite-dimensional systems, it emphasizes the importance of a more general view of infinite-dimensional ISS theory. This permits the analysis of more general system classes and provides new perspectives on and a better understanding of the classical ISS theory for ordinary differential equations (ODEs). Features of the book include:a comprehensive overview of the theoretical basis of ISS;
a description of the central applications of ISS in nonlinear control theory;
a detailed discussion of the role ofsmall-gain methods in the stability of nonlinear networks; and
an in-depth comparison of ISS for finite- and infinite-dimensional systems.
The book also provides a short overview of the ISS theory for other systems classes (partial differential equations, hybrid, impulsive, and time-delay systems) and surveys the available results for the important stability properties that are related to ISS.
The reader should have a basic knowledge of analysis, Lebesgue integration theory, linear algebra, and the theory of ODEs but requires no prior knowledge of dynamical systems or stability theory. The author introduces all the necessary ideas within the book.
Input-to-State Stability will interest researchers and graduate students studying nonlinear control from either a mathematical or engineering background. It is intended for active readers and contains numerous exercises of varying difficulty, which are integral to the text, complementing and widening the material developed in the monograph.
Reviews / Votes
"This book targets systems control theory experts willing to reinforce their understanding of nonlinear Lyapunov function techniques. It serves as a useful technical reference on ISS, a still active research trend that made its way into nonlinear systems control textbooks." (Didier Henrion, zbMATH 1555.93004, 2025)
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Person
Andrii Mironchenko
was born in 1986 in Odesa, Ukraine. He received the M.Sc. degree in applied mathematics from the Odesa I.I. Mechnikov National University, Odesa, Ukraine, in 2008; the Ph.D. degree in mathematics from the University of Bremen, Bremen, Germany in 2012, and the habilitation degree from the University of Passau, Germany, in 2023. He has held a research position with the University of Würzburg, Würzburg, Germany, and was a Postdoctoral Fellow of Japan Society for Promotion of Science (JSPS) with the Kyushu Institute of Technology, Fukuoka Prefecture, Japan (2013-2014). In 2014, he joined the Faculty of Mathematics and Computer Science, the University of Passau, Passau, Germany.
He is the (co)author of more than 60 peer-reviewed papers in journals and conference proceedings in control theory and applied mathematics. A. Mironchenko is a co-founder and co-organizer of the Workshop series "Stability and Control of Infinite-Dimensional Systems" (SCINDIS). He is a Senior Member of IEEE.
His research interests include stability theory, nonlinear systems theory, distributed parameter systems, hybrid systems, and applications of control theory to biological systems and distributed control.
Content
Chapter 1. Ordinary di?erential equations with measurable inputs.- Chapter 2. Input-to-state stability.- Chapter 3. Networks of input-to-state stable systems.- Chapter 4. Integral input-to-state stability.- Chapter 5. Robust nonlinear control and observation.- Chapter 6. Input-to-state stability of in?nite networks.- Chapter 7. Conclusion and outlook.- Index.