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**Dissipative systems analysis and control. Theory and applications.**
*(English)*
Zbl 0958.93002

Communications and Control Engineering Series. London: Springer. xi, 377 p. (2000).

The monograph consisting of 8 chapters, bibliography and index is devoted to dissipative systems theory and its applications in the control of linear and nonlinear continuous-time systems. This theory gives a framework for the analysis and synthesis of control systems by using an input-output approach based on energy-related considerations. After the introductory chapter, chapter 2 reviews the main results available for positive real linear systems and passive nonlinear systems. The applications of these ideas in stability analysis, stabilization and adaptive control of nonlinear systems are given. Chapter 3 presents the Kalman-Yakubovich-Popov (KYP) lemma including its applications in dissipativity, stability of closed-loop systems and absolute stability. Chapter 4 reviews the definitions and properties of dissipative systems such as passivity theorems, nonlinear KYP lemma, stability and stabilization issues, cascaded and linear delay systems. Chapter 5 presents a class of dissipative physical systems. Three different energy-based modeling system definitions are recalled: controlled Lagrangian, input-output Hamiltonian systems and port controlled Hamiltonian systems. A class of systems which has motivated a stabilizing control design by using passivity theory is treated. It corresponds to models in robotics. Chapter 6 is devoted to passivity-based control. The relations between dissipativity properties of the various systems presented in the previous chapter and the stability of the fixed point(s) are studied both for open-loop and closed-loop systems. Chapter 7 deals with direct adaptive control applied to mechanical and linear time invariant systems. Chapter 8 presents experimental results of the above methodology applied to two mechanical systems. An appendix surveys some basic results in Lyapunov stability and differential geometry theory.

The monograph is a self-contained advanced introduction to the theory which is consistently supplied with numerous physical examples. The book is intended primarily as a comprehensive state-of-the-art reference on dissipative systems theory with applications to control design mainly for physical systems. It will be suitable for graduate students interested in the control of linear and nonlinear systems as well as for researchers and practicing control engineers who are interested in applying this theory in their applications.

The monograph is a self-contained advanced introduction to the theory which is consistently supplied with numerous physical examples. The book is intended primarily as a comprehensive state-of-the-art reference on dissipative systems theory with applications to control design mainly for physical systems. It will be suitable for graduate students interested in the control of linear and nonlinear systems as well as for researchers and practicing control engineers who are interested in applying this theory in their applications.

Reviewer: LubomĂr Bakule (Barcelona)

### MSC:

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

93D15 | Stabilization of systems by feedback |

70Q05 | Control of mechanical systems |

93C40 | Adaptive control/observation systems |

93D10 | Popov-type stability of feedback systems |

93A30 | Mathematical modelling of systems (MSC2010) |