A. Kh. Gelig
Russia, 198904, Saint-Petersburg,
Petrodvoretz, Bibliotechnaya pl., 2,
Saint-Petersburg State University,
Department of mathematics and mechanics,
A system of differential-functional equations dz/dt = Az+bf, s = c'z, f = Ns is considered. Here A is a constant m×m-matrix, its n – 1 eigenvalues are in the left half-plane, one eigenvalue is zero, b and c are constant m-columns, N – nonlinear operator, wich describes pulse modulator dynamics. These equations describe a broad class of nonlinear impulse systems [1] with various kinds of modulation (amplitude, frequency, width etc.). Here s(t) is modulator's input, f(t) is modulator's output. By using the averaging method [1], by constructing the Lyapunov function as a fourth degree form and with help of V.A.Yakubovich's frequence theorem we received new frequency conditions of global stability for solution x = 0. Reference. 1. Gelig A.Kh., Churilov A.N. Stability and Oscillations of Nonlinear Pulse-Modulated Systems. Birkhäuser, Boston, 1998, 362 p.