Robust filtering for uncertain discrete-time systems: an improved LMI approach

This paper discusses the robust filtering problems for linear discrete-time systems with polytopic parameter uncertainty under the H₂ and H_∞ performance. We aim to derive a less conservative design than existing sufficient linear matrix inequality (LMI) based conditions. It is shown that a more efficient evaluation of robust H₂ or H_∞ performance can be obtained by a matrix inequality condition which contains additional free parameters as compared to existing characterizations. When applying this new matrix inequality condition to the robust filter design, these parameters give additional freedoms in optimizing the guaranteed H₂ or H_∞ performance. The optimization will then lead to a less conservative design. The results will recover the existing robust H₂ and H_∞ filtering ones when the additional free parameters are set to be zero. We also propose an iterative algorithm to further refine the suboptimal filter. Examples are given to demonstrate the less conservatism of the proposed approaches.