H-representation to stochastic observability conservation by output feedback and Gramian bounds

In this paper, we are concerned with uniform complete observability of linear stochastic time-varying systems conserved by output feedback and Gramian bounds via so called H-representation method. We obtain the lower and upper bounds for the Gramian of output feedback stochastic system from the original system and vice versa. A numerical example is constructed to verify the effectiveness of our main result. The uniform complete observability is useful for the analysis and synthesis of the Kalman filter.

Automated summary

This paper addresses the issue of uniform complete observability of linear stochastic time-varying systems under output feedback and Gramian bounds, using the H-representation method. The study obtains lower and upper bounds for the Gramian of the output feedback stochastic system from the original system, as well as the vice versa. A numerical example is provided to validate the effectiveness of the main result. Uniform complete observability is important for the analysis and synthesis of the Kalman filter.