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Volume 15,     Number 2,     Summer 2007

 

INVARIANT APPROACH TO AN EXISTENCE
PROBLEM OF NONTRIVIAL ASYMPTOTIC
STABILITY CONE
VASILIY YE. BELOZYOROV

Abstract. The description of algebraic invariants for an autonomous system of the ordinary quadratic differential equations is given. With the help of these invariants, an equivalence problem for quadratic systems of the second (and third) orders is solved. The existence invariant conditions of a nontrivial asymptotic stability cone for the regular system of quadratic differential equations of the second order are also indicated. Further, these conditions are used to design a linear feed-back for a bilinear system of the second order guaranteeing the ex- istence of the nontrivial asymptotic stability cone of the closed system. Quadratic systems all solutions of which are bounded, and it's boundedness do not depend on a kind of a linear part are also found.

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