On performance improvements of an inverted pendulum with noisy delay feedback controller

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 to study the stability regions in terms of the inverted pendulum´s parameters and to derive stability conditions. Demonstrations show that noise enhances the stability and reduces the influence of time delay.