# On finite-dimensional parametrizations of attainability sets

- Authors
- Journal
- Applied Mathematics and Computation 0096-3003
- Publisher
- Elsevier
- Publication Date
- Volume
- 78
- Identifiers
- DOI: 10.1016/0096-3003(96)00004-5

## Abstract

Abstract The attainability set is defined to be a finite-dimensional integral-type image of the set of all absolutely continuous scalar functions of time whose derivatives take values in a given interval. For a class of control systems with scalar controls restricted to the above interval (the class comprises, in particular, some bilinear systems), the attainability set has the traditional meaning. A method of finite-dimensional parametrization of the attainability set is described. The parametrization is universal, i.e., the same for all attainability sets of a fixed dimension. For the case of control systems, the result provides an upper estimate on the number of switchings sufficient to bring the system to an arbitrary reachable state at a prescribed time.

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