Sentence examples for generalized stability from inspiring English sources

We achieve the general solution and the generalized stability result for the following functional equation in random normed spaces (in the sense of Sherstnev) under arbitrary t-norms:, where for any fixed integer with.

Two of the best known functional equations for which there are no satisfactory results as regards generalized stability in the sense of Bourgin [1] and Găvruţa [2] are Fréchet's polynomial equations: D n p ( x 1, …, x n + 1 ) = 0, x 1, …, x n + 1 ∈ M (1.1).

There exist series of program packages for investigation and design of uncertain control systems based on the corresponding analytical methods, which r application allows either to verify the given system stability or to calculate the parameters deviations from the nominal values ensuring the system hurwitz or generalized stability.

Proof of generalized stability of functional equation based on (1) is elucidated as follows.

This type of stability is referred to as the generalized stability.

The unmodeled response is rejected by requiring robust performance with respect to a generalized stability region.

In this paper, we investigate four different types of Ulam stability, i.e., Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of nonlinear implicit fractional differential equations with non-instantaneous integral impulses and nonlinear integral boundary condition.

Furthermore, the design methods of state feedback controllers are considered such that the resulting closed-loop system has generalized quadratic stability with (H_{infty}) performance.

By using the linear matrix inequality (LMI) approach, a sufficient condition is presented for a prescribed uncertain singular system with time-delay to have generalized quadratic stability and (H_{infty}) performance.

It was shown by the numerical example that the proposed method can solve generalized quadratic stability with (H_{infty}) performance for the parameter uncertain continuous-time singular systems with state delay.

Recently, Baktash et al. [16], Cho et al. [17 20], Gordji et al. [21 24], Lee et al. [25, 26], Najati et al. [27, 28], Park et al. [29], Saadati et al. [30] and Savadkouhi et al. [31] have studied and generalized several stability problems of a large variety of functional equations.