Delay effects on stability. A robust control approach.

*(English)*Zbl 0997.93001
Lecture Notes in Control and Information Sciences. 269. London: Springer. xvi, 383 p. (2001).

From the author’s preface: The monograph is devoted to the effect of delays on the stability properties of dynamical systems. Stability regions with respect to the delay parameters are considered, and some sufficient or necessary and sufficient characterizations are proposed.

In the first chapter, the problem statement, the definition of the state, the existence of solutions, uniqueness, continuous dependence, stability definitions, etc. are presented. In the second chapter some engineering and biological examples are considered. The third chapter is devoted to the basic delay effect, notions in delay systems and propagation models. The fourth chapter addresses the frequency-domain for the analysis of dynamical systems including discrete ones, or some special classes of distributed delays. The fifth chapter is devoted to Lyapunov’s second method and its application. The sixth chapter deals with some robustness issues in closed-loop schemes. The last chapter is devoted to some applications.

In the first chapter, the problem statement, the definition of the state, the existence of solutions, uniqueness, continuous dependence, stability definitions, etc. are presented. In the second chapter some engineering and biological examples are considered. The third chapter is devoted to the basic delay effect, notions in delay systems and propagation models. The fourth chapter addresses the frequency-domain for the analysis of dynamical systems including discrete ones, or some special classes of distributed delays. The fifth chapter is devoted to Lyapunov’s second method and its application. The sixth chapter deals with some robustness issues in closed-loop schemes. The last chapter is devoted to some applications.

Reviewer: Tamaz Tadumadze (Tbilisi)

##### MSC:

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

93C23 | Control/observation systems governed by functional-differential equations |

34K20 | Stability theory of functional-differential equations |

93D15 | Stabilization of systems by feedback |

93D09 | Robust stability |

93C55 | Discrete-time control/observation systems |

34K40 | Neutral functional-differential equations |

34K06 | Linear functional-differential equations |