Mathematical Control Theory

Jerzy Zabczyk is Professor Emeritus at the Institute of Mathematics at the Polish Academy of Sciences in Warsaw, Poland. His research interests include deterministic and stochastic control theory, stochastic and deterministic partial differential equations, and mathematical finance. He is the author of more than ninety research papers, and seven mathematical books.

• Preface.- Preface to the second edition.- Introduction.- Part I. Elements of Classical Control Theory.- Chapter 1. Controllability and Observability.- Chapter 2. Stability and Stabilizability.- Chapter 3. Controllability with Vanishing Energy.- Chapter 4. Systems with Constraints.- Chapter 5. Realization Theory.- Part II. Nonlinear Control Systems.- Chapter 6. Controllability and Observability of Nonlinear Systems.- Chapter 7. Stability and Stabilizability.- Chapter 8. Realization Theory.- Part III. Optimal Control.- Chapter 9. Dynamic Programming.- Chapter 10. Viscosity Solutions of Bellman Equations.- Chapter 11. Dynamic Programming for Impulse Control.- Chapter 12. The Maximum Principle.- Chapter 13. The Existence of Optimal Strategies.- Part IV. Infinite-Dimensional Linear Systems.- Chapter 14. Linear Control Systems.- Chapter 15. Controllability.- Chapter 16. Stability and Stabilizability.- Chapter 17. Linear Regulators in Hilbert Spaces.- Chapter 18. Boundary Control Systems.- Appendix.- References.- Notations.- Index.

“It enables the reader to acquire a capability to construct and analyze biological systems. The mathematical exposition is clear and with detailed explanations of important ideas and interesting results. The book takes an expository approach where the continuous prose intersects with several carefully constructed diagrams and figures. … it contains an extensive list of references and can serve as a reference text for researchers in this field.” (Stéphanie Abou and Anita T. Layton, SIAM Review, Vol. 63 (4), December, 2021)“An appendix summarizes important mathematical background results. The treatment of both finite- and infinite-dimensional systems is a unique feature of the book … . the book remains largely a book on classical methods, though one of highest mathematical standards. The book is decidedly mathematical in style, with complete proofs of all results, stringent mathematical argumentation, and a traditional definition-theorem-proof structure. … this second edition of the classical text remains a highly valuable contribution to the field.” (Lars Grüne, SIAM Review, Vol. 63 (2), September, 2021)“This new edition should be a useful resource for students and researchers of control theory.” (IEEE Control Systems Magazine, Vol. 41 (2), April, 2021)