Set-theoretic methods in control.

*(English)*Zbl 1140.93001The book is an outstanding monograph of a recent research trend in control. It reflects the vast experience of the authors as well as their noticeable contributions to the development of this field. The material is organized in the following chapters: 1. Introduction; 2. Lyapunov and Lyapunov-like functions; 3. Convex sets and their representation; 4. Invariant sets; 5. Dynamic programming; 6. Set-theoretic analysis of dynamic systems; 7. Control of parameter-varying systems; 8. Control with time-domain constraints; 9. (Sub-)Optimal control; 10. Set-theoretic estimation; 11. Related topics (Adaptive control, The domain of attraction, Hybrid and switching systems, Planar systems); 12 Appendix (Euler auxiliary system, Software for the computation of invariant sets). At the conceptual level, the book was meant as a self contained volume for readers with the usual background in systems and control. The text is very accessible (the style is attractive; the theoretical concepts and results are accompanied by relevant examples so as to facilitate the deep understanding of the discussed topics; both analytical and numerical approaches are presented; the final section of each chapter includes exercises). The book is highly recommended to PhD students and researchers working in control engineering or applied mathematics. The material can also be used for graduate courses in these areas.

Reviewer: Octavian Pastravanu (Iaşi)

##### MSC:

93-02 | Research exposition (monographs, survey articles) pertaining to systems and control theory |

49-02 | Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control |

34D20 | Stability of solutions to ordinary differential equations |

49L20 | Dynamic programming in optimal control and differential games |

93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |

93D09 | Robust stability |

93D15 | Stabilization of systems by feedback |

93D20 | Asymptotic stability in control theory |

93D30 | Lyapunov and storage functions |