Exact observability and stability of stochastic implicit systems

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. (c) 2021 Elsevier B.V. All rights reserved.

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This paper discusses the exact observability and stability of stochastic implicit systems. Conditions for the existence and uniqueness of impulse solutions, necessary and sufficient conditions for exact observability, and stability conditions are derived using stochastic Laplace transform, matrix theory, and linear matrix inequalities. Examples are provided to illustrate the effectiveness of the theoretical results.