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**Local disturbance decoupling with stability for nonlinear systems.**
*(English)*
Zbl 0781.93019

Lecture Notes in Control and Information Sciences. 166. Berlin: Springer- Verlag. v, 135 p. (1991).

In the monograph the local disturbance decoupling problem with stability for nonlinear dynamical control systems is considered. Using the differential geometry methods several conditions under which there exists a locally defined static state feedback that decouples the outputs from the disturbances are formulated and proved. Moreover, it is required, that local feedback exponentially stabilizes the equilibrium of the modified system. Generally, the author proposes two methods for solving the decoupling problem, (Chapter 3 and 4, respectively). Disturbance decoupling problem with dynamic feedback is considered in Chapter 6. The relationships between the disturbances decoupling problem and the linearization of a nonlinear dynamical system are explained in Chapter 5. The book contains also many remarks and comments on stability, stabilizability and controllability problems arising in the theory of nonlinear dynamical systems. Illustrative, numerical examples are also presented. The monograph contains some open research problems for nonlinear dynamical systems. The extensive list of references contains 82 positions, mainly from the last ten years.

Reviewer: J.Klamka (Katowice)

### MSC:

93B27 | Geometric methods |

93C10 | Nonlinear systems in control theory |

93C15 | Control/observation systems governed by ordinary differential equations |

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

93B29 | Differential-geometric methods in systems theory (MSC2000) |

93B05 | Controllability |