Class Of Stochastic Delay Systems Research Articles

Delay‐dependent stability of a class of stochastic delay systems driven by G‐Brownian motion

This study discusses delay-dependent stability of a class of stochastic delay systems driven by G-Brownian motion in the sublinear expectation space. With the help of the degenerate Lyapunov functional, the mean square exponential stability and quasi-sure exponential stability criteria for stochastic delay systems driven by G-Brownian motion are established and an explicit upper bound of time delay is derived. In particular, for the delay-free case, the corresponding sufficient conditions are also obtained. Here, the stability conditions are directly related to the coefficients of the stochastic delay systems and are different from the existing stability conditions which are presented in terms of the G-Lyapunov function. Some examples are introduced to illustrate the delay-dependent stability criteria.

Adaptive state estimation for stochastic delay systems with state-dependent Markovian switching

This study is concerned with an adaptive state estimation problem for a class of stochastic delay systems with state-dependent Markovian switching. Since the upper bound of parameters related to a transition rate of stochastic Markovian jump system is assumed to be unknown, an adaption law is developed to estimate such an unknown parameter. A class of adaptive state estimator is proposed such that not only the estimated parameter is bounded almost surely but also the estimated state error is mean-square exponentially stable. Finally, a numerical example is given to show the validity of the results.