(Differencialnie Uravnenia i Protsesy Upravlenia)

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Русская версия

**Sergey Mikhailovich Khryashchev**

Saint-Petersburg State Polytechnic University,

Doctor of Physics and Mathematics, professor,

29 Politechnicheskaya,

195251, Saint-Petersburg, Russia

For dynamical polysystem we give a characterization of the controllability property which is a fundamental property for control theory. This characterization establishes a link between the controllability and recurrence. Basing on this connection we propose a control method called the method of inverse movements. This method is not directly associated with any special properties of control systems, and it can be applied to arbitrary control systems having the structural stability property. Existence of the sequence of inverse movements can be established for some special systems. In particular, by this method the angular controllability of state-linear control systems can be investigated. For such systems new controllability conditions in the terms of the spectral characteristic of the matrix function of the state-linear control system have been given. These conditions for specific systems can be tested by using computer graphics.

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*Chech. Math. J., 1972; V. 22.*No. 3: P. 490-494 - Katok A. B., Hasselblatt B.
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- Khryashchev S. M. Spektral'nyi metod issledovaniya upravlyaemosti dinamicheskikh sistem vblizi invariantnykh mnozhestv.
*Avtomatika i telemekhanika*, 1998; No. 3: P. 29 - 42. (In Russian) - Khryashchev S. M. Ob upravlyaemosti lineinykh po sostoyaniyam dinamicheskikh sistem. [Controllability of State-Linear Dynamic Systems].
*Avtomatika i telemekhanika*, 2000; No. 10: P. 59 - 71. (In Russian) - Khryashchev S. M. Proverka usloviy upravlyaemosty lineinykh po sostoyaniyam sistem s pomoshchyu paketa simvol'nykh vychisleniy MAPLE.
*Nauchno-tekhnicheskie vedomosty SPbSTU*, 2007; No. 1: P. 260 - 268. (In Russian) - Khryashchev S. M.
*Upravlenie dinamicheskimi sistemami. Metody issledovaniya sistem s regulyarnym i khaoticheskim povedeniem traektoriy*. LAP (LAMBERT Academic Publishing), 2011. 295 p. (in Russian)