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This paper is concerned with the observability of linear stochastic impulsive systems with multiplicative noise. The concept of 2 p th 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-representation technique. It shows that the linear stochastic impulsive system is 2 p th moment observability if and only if the expanded system is completely observable. Subsequently, a series of algebraic criteria and geometric criteria for 2 p th 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.

Moment observability and output feedback stabilisation for linear stochastic impulsive systems