This paper discusses the exact observability and stability of the stochastic implicit systems. Firstly, the conditions for the existence and uniqueness of the impulse solution to stochastic implicit systems are given by stochastic Laplace transform. Secondly, the necessary and sufficient conditions for the exact observability of stochastic implicit systems are derived by the matrix theory. Thirdly, the application of exact observability of the stochastic implicit systems to its stability is discussed and sufficient conditions for the stability of systems considered are derived in terms of linear matrix inequalities. Finally, some examples are given to illustrate the effectiveness of the obtained theoretical results.

本文讨论了随机隐式系统的精确可观测性和稳定性。首先，通过随机拉普拉斯变换给出了随机隐系统脉冲解存在唯一性的条件。其次，由矩阵理论推导出随机隐系统精确可观测性的充要条件。第三，讨论了随机隐式系统的精确可观性在其稳定性中的应用，并根据线性矩阵不等式推导出了所考虑系统稳定性的充分条件。最后给出了一些例子来说明所得理论结果的有效性。