Abstract
Author in the reference Mao (2016) designed a linear discrete time noise to exponentially stabilize an unstable differential system with the global Lipschitz condition, which essentially opened a new field of stochastic systems driven by discrete time noises. However, the global Lipschitz condition is over strict and the result of exponential convergence is excessively rapid for many systems. Hence we see the necessity to loosen it to the local Lipschitz condition and develop some new stability results. In the present paper, by the method of Lyapunov functionals, we not only investigate the exponential stability for hybrid stochastic differential systems driven by linear discrete time noises with the local Lipschitz condition, but also study the H∞ stability and asymptotic stability using some new techniques.