Sentence examples for the impulse time from inspiring English sources

Based on the generalized equation [13], in this article, we consider the effect of the impulse intensity and the impulse time on the mean square exponential and non-exponential asymptotic stability of impulsive stochastic Volterra equation.

The parameter estimation law is modelled by an impulse-free time-varying differential equation associated with the impulse time sequence for determining when the observer state is updated.

By choosing the impulse intensity and the impulse time, We find that is not necessary condition for the exponential asymptotic stability.

The impact energy I, Eq. 1, is the integral of the impact force g(t) over the impulse time interval (t 1 − t 0).

For impulsive differential systems, most researchers concern about two kinds of impulse times: fixed impulse times and varying impulse times, which mean that the impulse time is some functions of the 'state x' [7 9].

Here, is the change in state at the impulse time.

We establish exponential stability of nonlinear time-varying impulsive systems by employing Lyapunov functions with discontinuity at the impulse times.

In order to match the features of rolling bearing fault, the impulse time-frequency dictionary and modulation dictionary are constructed to form the double-dictionary by using the method of parameterized function model.

The impulse times satisfy,.

where x ∈ ℝ n, the impulse times {t k } satisfy 0 ≤ t0 < t1 < ⋯ < t k < ⋯ and limk→+∞t k = +∞, and x' denotes the right-hand derivative of x.

To address this, the PEI-IS is devised by multiplying a series of input shapers in the Laplace domain, of which the impulse times are slightly perturbed from those of the zero vibration (ZV) shaper.