It is shown that the resulting closed-loop system is finite-time stable in probability.
It is shown that the closed-loop system is practically stable in probability.
It is shown that the global asymptotically stable in probability can be achieved for the closed-loop system.
It is shown that, under small-gain type conditions for small signals, the resulting closed-loop system is globally asymptotically stable in probability.
The closed-loop system can be proved to be globally stable in probability and the states can be regulated to the origin almost surely.
A robust decentralized adaptive sliding mode controller is designed to guarantee the uncertain stochastic delayed Hopfield neural networks is globally asymptotically stable in probability.
Based on stochastic finite-time stability theorem, it is proved that the closed-loop system is globally finite-time stable in probability.
Distinctive from the global stability in probability or asymptotic stability in probability obtained in related work, the proposed design algorithm can guarantee the solution of the closed-loop system to be finite-time stable in probability.
In addition, the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin.
The state-feedback controller is designed by regarding Markovian switching as constant such that the closed-loop system has a unique solution, and the equilibrium is asymptotically stable in probability in the large.
Based on the estimation value, a disturbance observer based attenuation and rejection controller is constructed such that the closed-loop system is asymptotically bounded in mean square or asymptotically stable in probability under different conditions.
