This article investigates the practical fixed-time stability in probability (PFxT-SP) of stochastic nonlinear systems (SNS). First, a unified PFxT-SP criterion is developed by using the stochastic differential equatio...
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This article investigates the practical fixed-time stability in probability (PFxT-SP) of stochastic nonlinear systems (SNS). First, a unified PFxT-SP criterion is developed by using the stochastic differential equation theory and Lyapunov functional method. Building on this foundation, several specific judgment forms of the PFxT-SP are established and corresponding estimates for the settling times (ST) are obtained. Compared to general FxT-SP, PFxT-SP requires the system converge to a specific region within ST T, where the region and ST can be determined based on the system parameters, and they are independent of the initial values. Additionally, a unified practicalfixed-timestability (PFxT-S) criterion of deterministic systems and two specific judgments are presented. Furthermore, the PFxT synchronization of T-S fuzzy complex networks with and without diffusion term is investigated. Finally, the feasibility of the theoretical results are illustrated by some simulation examples.
This article deals with the fixed-time control design issue for stochastic multi-agent systems (MASs). First of all, anew practicalfixed-timestability criterion in probability is proposed. Compared with existing wor...
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This article deals with the fixed-time control design issue for stochastic multi-agent systems (MASs). First of all, anew practicalfixed-timestability criterion in probability is proposed. Compared with existing works, the settling time is exclusively determined by design parameters, signifying that it can be calculated with precision. Utilizing this stability criterion, a fixed-time control strategy for stochastic MASs is designed, principally leveraging the backstepping control techniques and the radial basis function neural networks (RBF NNs). Additionally, the singularity problem in the control scheme is avoided by exploiting L'H & ocirc;pital's rule. With the designed control strategy, the stochastic MASs achieve practicalfixed-timestability. Furthermore, the tracking errors converge to an adjustable range near zero. The effectiveness of the proposed control strategy is verified by a series numerical simulation.
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