Global output-feedback finite-time stabilization for a class of stochastic nonlinear cascaded systems

Abstract

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Mean almost periodicity and moment exponential stability of discrete-time stochastic shunting inhibitory cellular neural networks with time delays

“…Uncertain models described by stochastic differential equations have caused great concerns since they have wide applications in practice such as engineering, physics, chemistry and biology [3,4,11,18,27,46]. In the actual situations, uncertainties have a consequence on the performance of the neural networks.…”

Adaptive finite‐time stabilization of stochastic nonlinear systems with the powers of positive odd rational numbers

“…Remark 1. q i in system (2) is only a positive odd rational number, which implies that system (2) is more general than q i ≥ 1 in other works [32][33][34][35][36] and q i ≤ 1 in the works of Zhao and Zhao 37 and Liu et al 38 The relation (3) is borrowed from the work of Ding and Li. 39 Compared with the work of the aforementioned authors, 39 we consider general stochastic nonlinear systems with drift terms f i and diffusion terms g i , i = 1, … , n.…”

“…Other works [32][33][34] dealt with the finite-time stabilization problem by state feedback controller for stochastic high-order nonlinear systems with different system structures. Zhai 35 and Lan et al 36 considered finite-time output feedback stabilization problem for stochastic high-order nonlinear systems. For stochastic low-order nonlinear systems, Zhao and Zhao 37 considered finite-time state feedback stabilization; Liu et al 38 further solved finite-time output feedback control problem.…”

“…1. Since the powers of integrators are relaxed to all the positive odd rational numbers but not necessary only high order or low order, the Lyapunov functions in other works [32][33][34][35][36][37][38] are inapplicable. In this paper, we should construct the new Lyapunov function.…”

Continuous feedback stabilization for a class of affine stochastic nonlinear systems

“…Since the works, such as Khasminskii [13], Kushner [15] and Mao [22] established a solid foundation for the stochastic stability theory, the design of stabilization controller has been investigated widely for various stochastic nonlinear systems. Several results on state-feedback stabilization and output-feedback stabilization for various classes of stochastic nonlinear systems have been achieved in [1,5,8,16,17,32] and the references therein.…”