Moment observability and output feedback stabilisation for linear stochastic impulsive systems

Xin Chen, Shixian Luo and Wu-Hua Chen

International Journal of Systems Science, 2023, vol. 54, issue 5, 1015-1032

Abstract: This paper is concerned with the observability of linear stochastic impulsive systems with multiplicative noise. The concept of 2pth moment observability is first introduced. Then, to explore the moment observability, a deterministic expanded system is established for the linear stochastic impulsive systems by the generalised $ \mathcal {H} $ H-representation technique. It shows that the linear stochastic impulsive system is 2pth moment observability if and only if the expanded system is completely observable. Subsequently, a series of algebraic criteria and geometric criteria for 2pth moment observability of linear stochastic impulsive systems are established by analysing the solution of the expanded system. The impulsive observer-based stabilisation problem for linear stochastic systems is further studied based on these observability criteria. Finally, two numerical examples illustrate the proposed theoretical results.

Date: 2023
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DOI: 10.1080/00207721.2022.2158444

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