Strong convergence and exponential stability of stochastic differential equations with piecewise continuous arguments for non-globally Lipschitz continuous coefficients

Robustness Analysis of Exponential Stability of Neutral-Type Nonlinear Systems With Multi-Interference

“…Up to now, there have been quite a few characteristic investigations of control methods and dynamical behaviors for nonlinear systems [1]- [20], such as fixed-time control [1], event-triggered adaptive control [2], distributed control [3], piecewise control [4], fuzzy control [5], horizon control [6], U-control [7], passivity cascade technique-based control [8], stabilization control [9], iterative learning control [10], sliding set design [11], robustness control [12] and so forth. In addition, various dynamical behaviors of nonlinear systems have been explored [13]- [20], such as asymptotic stability [13], Mittag-Leffler stability [14], globally exponential stabilization [15], [16], synchronization [13], [17], dissipativity [18], robustness analysis [19], [20], etc. Nowadays, the characteristic application scenarios of nonlinear systems widely appears in reality, such as the computer-node information transmission, the circuit conduction, robot joint control, drive-by-wire control systems and so forth [21], [22], [23].…”

“…Robustness and GES for nonlinear systems are two hot research fields no matter in the past or present [15], [16], [19], [20], [24]- [29]. On the one hand, robustness is usually endowed with different meanings in diverse application scenarios.…”

“…So far, with a view to these three kinds of interference factors: PCA, NT and SD, some investigators researched the robustness or GES of nonlinear systems influenced by single interference factor, such as [6], [20], [24], [25], [26], [30], [33], [50], etc. Some investigators explored the robustness or GES of systems affected by dual interference factors, such as [16], [27], [28], [29], [51], [53] and so forth. In the above literatures, Ref.…”

“…Ref. [16] proposed a split-step θ-method and presented comparison results of the numerical and real solutions for the exponential stability of a class of stochastic differential equations. Ref.…”

“…First, (A1) and (A2) are the qualitative requirements of activation function f (•) and neutral function G(•) throughout the whole text.Next, (A3) is a symbolic representation of the interval length [θ p , θ p+1 ). Then, (A4) is an assumption which makes "1 − ξ > 0" true appeared in the denominator of (4) in Lemma 1, and (A4) is also the origin of θ 1 in(16). Besides, (A5) is an assumption which makes "F (1 + k/1 − k, k) < 1" true in (24) so as to ensure the existence of (26), and (A5) is also the origin of θ 2 in (16).…”