Some long-standing problems in delay systems are given an elegant and systematic new treatment in this book, which features a methodology developed by the authors. The authors' approach deals with control of nonlinear systems in the presence of long delays, with large and rapid variation in the actuation or sensing path, or in the presence of long delays affecting the internal state of a system. The material is based on predictor feedback and infinite-dimensional backstepping transformations for linear systems, and the authors guide the reader from the basic concepts all the way through to nonlinear systems with state-dependent delays on the input as well as on system states. All control designs are given by explicit formulae, making the book especially useful for engineers who are concerned with actual implementations, and are accompanied by Lyapunov-based analysis for establishing stability and performance guarantees.
Nikolaos Bekiaris-Liberis received his PhD from the University of California, San Diego, and is currently a postdoctoral scholar at the University of California, Berkeley. His research interests are in delay systems, distributed parameter systems, and nonlinear control. Miroslav Krstic is the Alspach endowed professor, founding director of the Cymer Center for Control Systems and Dynamics, and Associate Vice Chancellor for Research at the University of California, San Diego. He is a Fellow of IEEE and IFAC; a recipient of the PECASE, NSF Career and ONR Young Investigator Awards; and the winner of Axelby and Schuck Paper Prizes. He has held distinguished visiting professorships at the University of California, Berkeley, and with the Royal Academy of Engineering, UK. He has coauthored nine books, including Boundary Control of PDEs: A Course on Backstepping Designs (2008).
Preface; 1. Introduction; Part I: 2. Linear systems with input and state delays; 3. Linear systems with distributed delays; 4. Application: automotive catalysts; 5. Nonlinear systems with input delay; Part II: 6. Linear systems with time-varying input delay; 7. Robustness of linear constant-delay predictor feedback to time-varying delay perturbations; 8. Nonlinear systems with time-varying input delay; 9. Nonlinear systems with simultaneous time-varying delays on the input and the state; Part III: 10. Predictor feedback design when the delay is a function of the state; 11. Stability analysis for forward-complete systems with input delay; 12. Stability analysis for locally stabilizable systems with input delay; 13. Nonlinear systems with state delay; 14. Robustness of nonlinear constant-delay predictors to time- and state-dependent delay perturbations; 15. State-dependent delays that depend on delayed states; Appendix A. Basic inequalities; Appendix B. Input-to-output stability; Appendix C. Lyapunov stability, forward-completeness, and input-to-state stability; Appendix D. Parameter projection; Bibliography; Index.
A powerful methodology for control of nonlinear systems is presented, along with powerful applications to long-standing problems in delay systems.
