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基于线性随机分布参数系统新的数学描述形式,给出了相应的均方稳定定义.考虑边界条件及散度定理,将偏微分方程转化成常微分方程,基于常微分方程的稳定性条件给出了相应偏微分方程的稳定性条件,从而得到了该类线性随机分布参数系统均方稳定的充要条件.最后通过仿真实例证明了结果的正确性.
Based on the new mathematical description form of the linear stochastic distributed parameter system, the corresponding definition of mean square stability is given. By considering the boundary conditions and the divergence theorem, partial differential equations are transformed into ordinary differential equations and the stability conditions based on ordinary differential equations are given The necessary and sufficient conditions for the mean square stability of the linear stochastic distributed parameter system are obtained.Finally, the simulation results show the correctness of the results.