Abstract
This paper mainly investigates stabilization of hybrid stochastic differential equations (SDEs) via periodically intermittent feedback controls based on discrete-time state observations with a time delay. First, by using the theory of M-matrix and intermittent control strategy, we establish sufficient conditions for the stability of hybrid SDEs. Then, we prove the intermittent stabilization for a given unstable nonlinear hybrid SDE by comparison theorem. Two numerical examples are discussed to support our results of theoretical analysis.
Highlights
Stochastic systems have been applied to model practical problems in many fields such as science and technology, information engineering, social economy and so on
Dong [12] discussed almost sure exponential stabilization by stochastic feedback control based on discrete-time observations
The stabilization problem by intermittent feedback controls based on discrete-time observations with a time delay could be transferred to the classic stabilization problem by intermittent feedback controls without discrete-time observations state and delay, the form of function is as follows (3.1)
Summary
Stochastic systems have been applied to model practical problems in many fields such as science and technology, information engineering, social economy and so on. Regular feedback controls are designed based on the continuous-time observations of current state x(t ) To reduce the high cost of continuous-time state observations, Mao [9] introduced the feedback controls based on discrete-time state observations to stabilize the given hybrid stochastic system. Mao et al [10] improved method to study the discrete-time state feedback control system, and stabilize a given hybrid stochastic systems in the sense of mean-square exponential stability. Dong [12] discussed almost sure exponential stabilization by stochastic feedback control based on discrete-time observations. Chen et al [13] studied stabilization of hybrid neutral stochastic differential delay equations by delay feedback control. Mao et al [14] and Hu et al [15] investigated stabilization of hybrid SDEs by delay feedback control. Qiu et al [17] and Zhu et al [18] took both discrete time and delay into account when designing the controller, they studied
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