Noise suppresses or expresses exponential growth

In this paper we will show that noise can make a given system whose solutions grow exponentially become a new system whose solutions will grow at most polynomially. On the other hand, we will also show that noise can make a given system whose solutions are bounded become a new system whose solutions will grow exponentially. In other words, we reveal that the noise can suppress or expresses exponential growth

Noise expresses exponential growth under regime switching

Consider a given system under regime switching whose solution grows at most polynomially, and suppose that the system is subject to environmental noise in some regimes. Can the regime switching and the environmental noise work together to make the system change signicantly? The answer is yes. In this paper, we will show that the regime switching and the environmental noise will make the original system whose solution grows at most polynomially become a new system whose solution will grow exponentially. In other words, we reveal that the regime switching and the environmental noise will exppress the exponential growth

Output-Feedback Stabilization Control of Systems with Random Switchings and State Jumps

The work is concerned with output-feedback stabilization control problem for a class of systems with random switchings and state jumps. The switching signal is supposed to obey Poisson distribution. Firstly, based on the asymptotical property of the distribution of switching points, we derive some sufficient conditions to guarantee the closed-loop system to be almost surely exponentially stable. Then, we pose a parametrization approach to convert the construction conditions of the output-feedback control into a family of matrix inequalities. Finally, a simulation example is given to demonstrate the effectiveness of our method

Almost sure stability with general decay rate of neutral stochastic pantograph equations with Markovian switching

This paper focuses on the general decay stability of nonlinear neutral stochastic pantograph equations with Markovian switching (NSPEwMSs). Under the local Lipschitz condition and non-linear growth condition, the existence and almost sure stability with general decay of the solution for NSPEwMSs are investigated. By means of M-matrix theory, some sufficient conditions on the general decay stability are also established for NSPEwMSs