| Abstract: | Absrtract The paper considers a continuous system with an m × m matrix A(·) having bounded entries, which are functionals of arbitrary nature. One knows only the range of variation of the coefficients. It is supposed that the local theorem of existence of a solution is satisfied and that any solution remaining in the bounded domain admits an extension for all t > 0. A Lyapunov function, which is given as a quadratic form with Jacobian matrix of the coefficients, is used to obtain relations between the limits of variation of the system coefficients, within which the system is exponentially stable in the large. We also study a pulse system, which is derived from the original one by replacing the entries along the main diagonal by synchronous pulse modulators effecting an amplitude frequency modulation. After the signals are averaged at the outputs of the modulators and the pulsing frequencies are assumed to tend to infinity, this system changes to the continuous system considered. For a pulse system, we obtain conditions on the range of variation of the coefficients and find lower bound for pulsation frequency assuring that the system is stable in the large. Original Russian Text ? I.E. Zuber, A.Kh. Gelig, 2009, published in Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya, 2009, No. 2, pp. 23–30. |
