Authors’ reply to “Comments on ‘Finite-time stability theorem of stochastic nonlinear systems [Automatica 46 (2010) 2105–2108]”’

Finite-time stochastic input-to-state stability of switched stochastic nonlinear systems

“…Both of them are on the criteria of finite-time stability of SNL systems. But there are two obvious different points: 1) system (4) which we considered is non autonomous, while system (1) in [2], [3] is autonomous; 2) there is a GKL function in the proof of our Theorem 3.1 and corresponding Definition 2.3, which means that the FGSP problem is considered quantitatively; while, in [2], [3], the same problem is considered qualitatively.…”

“…So, the study of finite-time globally asymptotical stability (GAS) is very helpful to the study of FISS. In [2], [3] and [28], the definition of finite-time globally asymptotical stability in probability (FGSP) was provided and some criteria have been given. But, in [2], [3] and [28], the definition of FGSP was defined in the form of stability in probability plus attractivity in probability.…”

“…In [2], [3] and [28], the definition of finite-time globally asymptotical stability in probability (FGSP) was provided and some criteria have been given. But, in [2], [3] and [28], the definition of FGSP was defined in the form of stability in probability plus attractivity in probability. To study the FSISS of stochastic systems, a definition of FGSP in the form of GKL function (|x| ≤ β(|x 0 |, t), where x is the system state and x 0 is the initial value and β is a GKL function) is needed.…”

Finite‐time synchronization for memristor‐based BAM neural networks with stochastic perturbations and time‐varying delays

“…Furthermore, in the biological neural system, the transfer of information among synapses always has stochastic perturbations, which come from the disturbance of the internal structure parameters, the errors caused by random measurement, external environment interference, etc. Therefore, the system model considering stochastic factors, which is called stochastic system, can describe the actual system more accurately and get extensive attention and research . Neural networks with stochastic perturbations and time‐varying delays have more richer dynamic properties, and the analytical method is more complex and more practical.…”

Finite Time Inverse Optimal Stabilization for Stochastic Nonlinear Systems

“…After the success of finite time stability and stabilization theory for deterministic systems, how to extend them to the case of stochastic systems naturally became an important research area. Chen and Jiao [18][19][20] presented a new concept of finite time stability for stochastic nonlinear systems, and a theorem concerning the finite time stability was proved. However, to the authors knowledge, no work on finite time inverse optimal stabilization for stochastic systems has been done at the present stage.…”