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摘要：In this talk, a new type stability theorems

for stochastic systems and its application to stochastic stabilization are

introduced. Firstly, a new type of stability theorem for stochastic systems is

introduced. Based on this stability theorem and its corollaries, stochastic

stabilization and destabilization by noise are further investigated. In the

work, the local Lipschitz condition is weakened to the generalized local

Lipschitz condition. The commonly used linear growth condition or one-side

linear growth condition is weakened to the generalized one-side linear growth

condition, which is local, variable and nonlinear, admits nearly arbitrary

variability in the time and real nonlinearity in the state. As an application,

a simple and direct design method is proposed for finding a noise strength ^

g(t; x) so that the added noise g(t; x)dB(t) stabilizes an unstable stochastic

system or destabilizes a stable one. A numerical example is presented at the

end of the note to illustrate the usage and efficiency of the proposed design

method.