Almost sure stability condition of weakly coupled linear nonautonomous random systems

In this study, the sufficient condition of almost sure stability of twodimensional oscillating systems under parametric excitations is investigated. The systems considered are assumed to be composed of two weakly coupled subsystems. The driving actions are considered to be stationary stochastic processes satisfying ergodic properties. The properties of quadratic forms are used in conjunction with the bounds for the eigenvalues to obtain, in a closed form, the sufficient condition for the almost sure stability of the systems.

Almost sure exponential stability of neutral stochastic delayed cellular neural networks

In this paper, almost sure exponential stability of neutral delayed cellular neural networks which are in the noised environment is studied by decomposing the state space to sub-regions in view of the saturation linearity of output functions of neurons of the cellular neural networks. Some algebraic criteria are obtained and easily verified. Some examples are given to illustrate the correctness of the results obtained.

Razumikhin-Type Theorems on General Decay Stability of Impulsive Stochastic Functional Differential Systems with Markovian Switching

In this paper, the Razumikhin approach is applied to the study of both p-th moment and almost sure stability on a general decay for a class of impulsive stochastic functional differential systems with Markovian switching. Based on the Lyapunov-Razumikhin methods, some sufficient conditions are derived to check the stability of impulsive stochastic functional differential systems with Markovian switching. One numerical example is provided to demonstrate the effectiveness of the results.

THE PROBABILITY STABILITY OF VISCOELASTIC PLATES

The almost sure stability of homogeneous viscoelastic platessubjected to a random wide-band stationary in-plane load isinvestigated. The viscoelastic behavior of the plate is described interms of the Bo- ltzmann superposition principle, the relaxationkernels of which are represented by the sums of exponents. On theassumption that the in-plane load is random wide-band stationaryprocess, sufficient conditions for al- Most sure stability ofviscoelastic plates are obtained by the applications of Lyapunov'sdirect method.

ON EXPONENTIAL STABILITY OF NON-AUTONOMOUS STOCHASTIC SEMILINEAR EVOLUTION EQUATIONS

Sufficient conditions for the exponential stability of a class of nonlinear, non-autonomous stochastic differential equations in infinite dimensions are studied. The analysis consists of introducing a suitable approximating solution systems and usig a limiting argument to pass on stability of strong solutions to mild ones. Consequently, under these conditions the random attractors of given stochastic systems are reduced to zero with exponential decay. Lastly, two examples are investigated to illustrate the theory.

ALMOST SURE AND MOMENT EXPONENTIAL STABILITY OF PREDICTOR-CORRECTOR METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS

This paper deals with almost sure and moment exponential stability of a class of predictor- corrector methods applied to the stochastic differential equations of Ito-type. Stability criteria for this type of methods are derived. The methods are shown to maintain almost sure and moment exponential stability for all sufficiently small timesteps under appropriate conditions. A numerical experiment further testifies these theoretical results.

Stabilization Control for Linear Switching Stochastic Systems Against Time-Delay in Communication Channel

The paper is concerned with stabilization problem for a class of stochastic switching systems with time-delay in the detection of switching signal. By using binomial model,Poisson process,and Wiener process to describe time-delay, switching signal, and exogenous disturbance, respectively, the system under investigation is entirely set in a stochastic framework. The influence of the random time-delay is combined into reconstructing the switching signal of overall closed-loop system and changes the distribution property of switching points. Therefore,based on the asymptotical behaviors of Poisson processes and Wiener processes,the almost surely exponential stability conditions are established. Furthermore,a design methodology is posed for solving the stabilization control.

Dynamic analysis of stochastic delayed cellular neural networks

The stability of stochastic delayed cellular neural networks(DCNNs) is investigated in this paper. Under the help of Lyapunov functional and the semimartingale convergence theorem, some sufficient criteria were obtained to check the almost sure exponential stability of the DCNNs.

Exponential Stability for Time-changed Stochastic Differential Equations

So far there have been few results presented on the exponential stability for time-changed stochastic differential equations.The main aim of this work is to fill this gap.By making use of general Lyapunov methods and time-changed Itôformula,we establish the exponential stability and almost sure exponential stability of solution to time-changed SDEs.Finally,we construct some examples to illustrate the effectiveness of our established theory.

EXPONENTIAL STABILITY FOR A CLASS OF SWITCHED STOCHASTIC SYSTEMS

In this paper, the stability properties for a class of switched stochastic systems with commutative componentwise subsystem matrices are studied. Under some switching law, the trivial solutions of the above systems are proved to be exponentially stable in mean square and almost sure exponentially stable if the random perturbations are sufficiently “small”.