Sentence examples for using an integral inequality from inspiring English sources
For the nominal system (2.18), we will give a stability condition by using an integral inequality approach as follows.
In this section, the exponential stability in mean square for system (2.2) with initial conditions (2.3) and (2.4) is shown by using an integral inequality.
In this paper, by using an integral inequality, we establish some sufficient conditions ensuring the existence and p-exponential stability of periodic solutions for a class of stochastic shunting inhibitory cellular neural networks (SICNNs) with distributed delays.
To study the boundedness of solutions for some nonautonomous second order linear differential equations, Ou-Iang [1] used a nonlinear integral inequality.
Inequality (5) is called an integral inequality.
Grüss developed an integral inequality [1] in 1935.
In particular, we concentrate on constructing a delay- and basis- dependent Lyapunov Krasovskii function which is in favor of reducing the conservatism, and furthermore, by using the integral inequality method and the Projection Lemma, the peak-to-peak performance criterion is first established.
From the hypotheses and by using Jensen integral inequality and the inverse Hölder integral inequality, we have (2.17).
By using Jensen integral inequality (see [11]) and inverse Hölder integral inequality (see [12]) and noticing that are real-valued super-multiplicative functions, it is easy to observe that (2.10).
In this article, the problem of global exponential synchronization is investigated for the class of BAM NNs with time-varying and distributed delays and reaction-diffusion terms by using Poincaré integral inequality, Young inequality technique, and Lyapunov method, which are very important in theories and applications and also are a very challenging problem.
By using this new integral inequality and free-weighting matrix technique, a simpler L2 L∞ performance analysis result with fewer dimensions of linear matrix inequality (LMI) and fewer variables is presented.
