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For an end fixed inverted pendulum, the influence of time delay and effects of noise are studied in the sense of almost surely exponentially stable in this paper. Both time delay and noise are ubiquitous in control systems. Time delay usually does harm to the stability of systems while noise is helpful in some particular cases. The so-called domain subdivision approach and the Ito formula are adopted...
For a stochastic delay differential equation, the effects of noise and time delay are discussed in the sense of mean square stability. Neither time delay nor noise play bad roles for the differential equations and both of them are ubiquitous in nature. The so-called domain subdivision approach is taken to study the stability regions in terms of the parameters of a given equation and the Ito formula...
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