Stochastic stabilization of hybrid differential equations

Stochastic stabilization of singular systems with Markovian switchings

“…In other words, one could design a controller in terms of a Brownian noise perturbation to stabilize an SMJS, which also guarantees the solution unique. From Theorems 1 and 2, it is seen that the steady state distribution k 1 is assumed to be available exactly, which is same to the ones in [44,45]. It means that the TRM K should also be known exactly.…”

“…That is because the other conditions can be obtained similarly and will be omitted here. By substituting the representations of Y i defined in (47) and X described in (45) into (41), we have…”

“…In references [40][41][42][43], it has been proved that a Brownian noise perturbation referred to a controller in the diffusion section can stabilize or destabilize a system which cannot be stabilized by a regular controller. If the underlying system has jumping parameters, the stochastic stabilization problem was considered in [44,45]. By investigating these references, it is seen that they are all about normal stochastic systems.…”

Exponential p-convergence analysis for stochastic BAM neural networks with time-varying and infinite distributed delays

“…On the other hand, systems in many branches of science and industry not only depend on time delays including time-varying delays and infinite distributed delays but also various types of stochastic environmental noise, and systems could be stabilized or destabilized by certain stochastic inputs [40]. Therefore, it is of significant importance to consider stochastic effects for the neural networks.…”

pth moment exponential stability of hybrid stochastic fourth-order parabolic equations

“…All authors read and approved the final manuscript. 1 Tongda College of Nanjing University of Posts and Telecommunications, Yangzhou, Jiangsu 225127, China. 2 School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Nanjing, Jiangsu 210023, China.…”