Nonlinear control systems. An algebraic setting.

*(English)*Zbl 0920.93002
Lecture Notes in Control and Information Sciences. 242. London: Springer. xvi, 169 p. (1999).

The aim of this book is to give an account of the algebraic approach to nonlinear control systems, and a comprehensive description of the techniques and tools which are necessary for the investigation of different problems.

The general setting and the fundamental notions are described and illustrated in the first part of the book. The authors introduce the notion of differential form in an abstract and formal way and they characterize properties such as accessibility, controllability and observability. The structure algorithm and a canonical decomposition of the nonlinear system are given. A generalized state-space transformation and a regular generalized state feedback are presented as well.

In the second part of the book, the tools and techniques of the algebraic approach are used for solving a number of basic problems which are encountered in process control. The authors solve the Feedback Linearization Problem, in terms of the accessibility filtration. The output filtration and the structure algorithm established in the first part are employed for solving both the Noninteracting Control Problem and the Model Matching Problem. Also, the Disturbance Decoupling Problem is solved using the subspace which is observable independently from the input.

In the third part, the results of the first part are analyzed from a differential algebraic point of view. For this purpose, differential algebraic tools are introduced and a certain differential field is associated to the state space system. The account is intelligible and accompanied by suggestive examples.

The general setting and the fundamental notions are described and illustrated in the first part of the book. The authors introduce the notion of differential form in an abstract and formal way and they characterize properties such as accessibility, controllability and observability. The structure algorithm and a canonical decomposition of the nonlinear system are given. A generalized state-space transformation and a regular generalized state feedback are presented as well.

In the second part of the book, the tools and techniques of the algebraic approach are used for solving a number of basic problems which are encountered in process control. The authors solve the Feedback Linearization Problem, in terms of the accessibility filtration. The output filtration and the structure algorithm established in the first part are employed for solving both the Noninteracting Control Problem and the Model Matching Problem. Also, the Disturbance Decoupling Problem is solved using the subspace which is observable independently from the input.

In the third part, the results of the first part are analyzed from a differential algebraic point of view. For this purpose, differential algebraic tools are introduced and a certain differential field is associated to the state space system. The account is intelligible and accompanied by suggestive examples.

Reviewer: M.Ivanovici (Craiova)

##### MSC:

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

93C10 | Nonlinear systems in control theory |

93B25 | Algebraic methods |