## Abstract

A system S of vector fields is locally controllable at point p if, for every positive time t, the set of points reachable from p by an S-trajectory in time less than equivalent to t contains p in its interior. Let K be the convex hull of the values X(p) of those X belonging to S for which X(p) does not equal 0. It is well known that S is 1. c. at p if o belongs to interior (K), and that S is not 1. c. at p if 0 does not belong to K. It is proved that these are the only cases in which it is possible to determine if S is 1. c. at p by just looking at the values at p of the elements of S. A sufficient condition is proved for local controllability which gives new information for the case when 0 belongs to K but 0 does not belong to interior (K).

Original language | English (US) |
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Pages (from-to) | 790-802 |

Number of pages | 13 |

Journal | SIAM Journal on Control and Optimization |

Volume | 16 |

Issue number | 5 |

DOIs | |

State | Published - 1978 |

## All Science Journal Classification (ASJC) codes

- Control and Optimization
- Applied Mathematics