Vol.2, No 9, 1999 pp. 847-855
UDC: 531.011 534
ALGEBRAIC CRITERIA FOR ASYMPTOTIC STABILITY
AT 1:1 RESONANCE
IN THE CASE OF SIGN-CONSTANT LYAPUNOV FUNCTION
P. S. Krasil'nikov
Department of Theoretical Mechanics, Moscow Aviation Institute,
125871 Moscow, Volokolamskoe 4, Russia
Abstract. In the critical case
of two pairs of purely imaginary eigenvalues at 1:1 resonance, the asymptotic
stability of a system with two degrees of freedom is investigated. It is
assumed that eigenvalues have simple elementary divisors. By means of sign-constant
Lyapunov function which has sign-constant derivative, the new aalgebraic
critria of asymptotic stability is obtained.
ALGEBARSKI KRITERIJUM ZA ASIMPTOTSKU STABILNOST
PRI REZONANCIJI 1:1 ZA SLUČAJ KONSTANTNOG ZNAKA LJAPUNOV-LJEVE FUNKCIJE
Istraživana je asimptotska stabilnost sistema sa dva stepena
slobode za kritični slučaj dve čisto imaginarne sopstvene vrednosti pri
1:1 rezonanciji. Pretpostavljeno je da sopstvene vrednosti imaju proste
elementarne delioce. Pomoću Liapunov-ljeve funkcije konstantnog znaka sa
konstantnim znakom izvoda, dobijen je novi algebarski kriterijum asimptotske
stabilnosti.
