Consider a system of functional differential equations
dz/dt=Az+bf, s=c'z, f=Ns,
where A is a constant (m × m) - matrix,
all the eigenvalues of which, except for that to be zero, lay
in the left semiplane, b and c are constant m-dimensional columns,
N is a nonlinear operator describing a dynamic pulse modulator.
These equations describe a wide class of nonlinear pulse systems with different types of pulse modulation (amplitude, pulse-width, frequency, and so on). In this case s(t) is a signal at the modulator input, f(t) is a signal at the its output.
By means of the analysis of Lyapunov functions in terms of the quartic forms and the averaging method [1] a new frequency criterion of stability of functional differential equations, describing the dynamic of nonlinear pulse systems in the case of one zero root of a characteristic equation with monotonic differentiable nonlinear characteristic, is obtained.
Reference
1. Gelig A.Kh., Churilov A.N. Stability and Oscillations of
Nonlinear Pulse-Modulated Systems. Birkhauser, Boston,
1998, 362 p.