A novel H_∞ filtering for uncertain systems with multiplicative noise

In this paper, a novel robust H_∞ filtering for uncertain systems with multiplicative noise is developed. Krein space approach is proposed to handle with a robust H_∞ problem. To this end, a new Krein space formal system is designed according to the partially equivalent relation between the error Gramian in Krein space and the objective H_∞ problem. Consequently, filter gain of estimate recursions can be obtained through Krein space formal system if an existence condition is satisfied. In addition, the parameter uncertainty, entering into both state and measurement equations, satisfies an energy-type constraint. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.