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

Abstract

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 ‐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.