Krein space approach to robust filtering for multiple uncertain systems

In this paper, a new Krein space approach to robust filtering for linear systems with multiple uncertainties is developed. The multiple uncertainties satisfy the energy-type constraints, entering into both state and measurement equations. The proposed approach is used to tackle the sub-optimization problem arising from a sum quadratic constraint (SQC) of system uncertainties. To this end, a novel Krein space formal system is designed. Then recursive estimation is derived from the formal system. Also, the necessary and sufficient condition for the estimation to be optimal is proposed. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.