In this paper, we study the almost sure stability of discretetime jump linear systems with a finite-state Markov-form process. A general condition for almost sure stability, which is a necessary and sufficient condition for (scalar) one-dimensional systems, is derived. Many simpler testable sufficient conditions for almost sure stability are derived from this sufficient condition.

To the best of our knowledge, there are only few results on general decay stability applied to stochastic neural networks. In the paper, we study both the pth moment ðpZ2Þ and the almost sure stability on a general decay rate for impulsive stochastic Cohen–Grossberg neural networks with mixed time delays. The presented theory allows us to study the pth moment stability even if the exponential s...

Recently, Mao [19] initiates the study the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations by feedback controls based on discrete-time state observations. Mao [19] also obtains an upper bound on the duration τ between two consecutive state observations. However, it is due to the general technique used there that the bound on τ is not very sharp....

We deduce almost-sure exponentially fast mixing of passive scalars advected by solutions the stochastically-forced 2D Navier–Stokes equations and 3D hyper-viscous in Td subjected to nondenegenerate H?-regular noise for any ? sufficiently large. That is, all s>0 there is a deterministic exponential decay rate such that mean-zero Hs H?s at this same with probability one. This equivalent what know...

A new dynamical model is developed here to study the stochastic stability of Fault Tolerant Control Systems (FTCS) with multiple failure processes. In particular, two independent failure processes with Markovian characteristics are considered: one for plant component failures and the other for actuator failures. In this model, the Fault Detection and Isolation (FDI) process is also formulated a...

For a stochastic differential equation SVIR epidemic model with vaccination, we prove almost sure exponential stability of the disease-free equilibrium for ℛ(0) < 1, where ℛ(0) denotes the basic reproduction number of the underlying deterministic model. We study an optimal control problem for the stochastic model as well as for the underlying deterministic model. In order to solve the stochasti...