# Aleksei Fedorovich Filippov

**Aleksei Fedorovich Filippov** (Russian: Алексей Фёдорович Филиппов; 29 September 1923 – 10 October 2006) was a Russian mathematician, who worked on differential equations, differential inclusions, diffraction theory, and numerical methods.

Aleksei F. Filippov | |
---|---|

Born | |

Died | 10 October 2006 | (aged 83)

Nationality | Russia |

Alma mater | Moscow State University |

Known for | Filippov's lemma Curve theorem proof |

Scientific career | |

Fields | Mathematics |

Institutions | Moscow State University |

Doctoral advisor | Ivan G. Petrovsky |

A. F. Filippov was born in Moscow in 1923. After serving in the Red Army during the Second World War he attended Moscow State University (Faculty of Mechanics and Mathematics). After graduating from the university in 1950, he worked there until his death in 2006 (a professor since 1978). He got his Ph.D. under the supervision of I. G. Petrovsky.

Filippov showed interest in continuous loops in 1950 when he constructed a proof that they divide a plane into interior and exterior parts.^{[1]} Known as the Jordan curve theorem, it exemplifies a mathematical proposition easily stated but difficult to prove.

In 1955 Filippov and V. S. Ryaben'kii became interested in difference equations and wrote *On the Stability of Difference Equations*.^{[2]} The work was developed into a textbook in 1961 which was used in Moscow State University and many other Russian universities for several decades.^{[3]}
In 1959 he published a paper containing a lemma about implicit functions designed for use in optimal control theory which is named after him (*Filippov's lemma*).^{[4]}^{[5]}^{[6]}

Filippov made an important contribution in the theory of discontinuous ordinary differential equations with his monograph *Differential Equations with Discontinuous Righthand Sides* (1985).^{[7]} Such set-valued dynamical systems arise in sliding mode control, an important class of feedback control systems demonstrating robust control. Such systems model some mechanical systems with Coulomb friction, and more recently genetic networks.

A. F. Filippov was awarded the Moscow State University's Lomonosov Award in 1993.

## ReferencesEdit

**^**A.F. Filippov (1950) An elementary proof of Jordan's theorem,*Uspekhi Matematischeskikh Nauk*5(39):173–6, link from All-Russian Mathematical Portal**^**Review by W.J. Trjitzinsky: MR0068009**^**U.W. Hochstrasser review: MR0090757**^**A.F. Filippov (1959) "On certain questions in the theory of optimal control", Journal of the Society for Industrial and Applied Mathematics Control, Series A, 1:76–84**^**E.J. McShane & R.B. Warfield Jr. (1967) On Filippov's Implicit Functions Lemma,*Proceedings of the American Mathematical Society***^**S. Nababan (1979) "A Filippov-type lemma for functions involving delays and its application to time-delayed optimal control problems",*Journal of Optimization Theory and Applications*27(3):357–76**^**A.F. Filippov (1985) Differential Equations with Discontinuous Righthand Sides, Kluwer Academic Publishers, link from Google Books, review by J. Jarník: MR0790682

## External linksEdit

- Aleksei Fedorovich Filippov at the Mathematics Genealogy Project
- All-Russian Mathematical Portal
- Russian Encyclopedia: Filippov, Aleksei Fedorovich (in Russian)
- Izobov, N. A.; et al. (1998) "Alekseĭ Fedorovich Filippov" (on the occasion of his 75th anniversary).
*Differential Equations*34, no. 10, 1297–1302.