Blanchini F., Miani S. Set-Theoretic Methods in Control

2nd Edition. — Springer International Publishing, Switzerland, 2015. — 640 p. – (Systems & Control: Foundations & Applications) — ISBN: 3319179322.The second edition of this monograph describes the set-theoretic approach for the control and analysis of dynamic systems, both from a theoretical and practical standpoint. This approach is linked to fundamental control problems, such as Lyapunov stability analysis and stabilization, optimal control, control under constraints, persistent disturbance rejection, and uncertain systems analysis and synthesis. Completely self-contained, this book provides a solid foundation of mathematical techniques and applications, extensive references to the relevant literature, and numerous avenues for further theoretical study.
All the material from the first edition has been updated to reflect the most recent developments in the field, and a new chapter on switching systems has been added. Each chapter contains examples, case studies, and exercises to allow for a better understanding of theoretical concepts by practical application. The mathematical language is kept to the minimum level necessary for the adequate formulation and statement of the main concepts, yet allowing for a detailed exposition of the numerical algorithms for the solution of the proposed problems.
Set-Theoretic Methods in Control will appeal to both researchers and practitioners in control engineering and applied mathematics. It is also well-suited as a textbook for graduate students in these areas.Lyapunov and Lyapunov-like functions.
Convex sets and their representation.
Invariantsets.
Dynamic programming.
Set-theoretic analysis of dynamic systems.
Control of parameter-varying systems.
Control with time-domain constraints.
Switching and switched systems.
(Sub-)Optimal Control.
Set-theoretic estimation.
Related topics.
Appendix.
Remarkable properties of the Euler auxiliary system.
MAXIS-G: a software for the computation of invariant sets for constrained LPV systems.