pth Moment Asymptotic Stability/Stabilization and pth Moment Observability of Linear Stochastic Systems: Generalized ℋ-Representation

This article develops a generalized $\mathcal {H}$ -representation, which can transforms stochastic systems into deterministic systems. With the help of this new approach, the necessary and sufficient conditions of $p$ th moment asymptotic stability and stabilization of linear stochastic systems are addressed. Meanwhile, the generalized $\mathcal {H}$ -representation method is also applied to investigate $p$ th moment observability and $p$ th moment complete observability for the addressed systems.