Improved robust H₂and H_∞filtering for uncertain discrete-time systems

This paper is concerned with the robust H2and H∞filtering problems for linear discrete-time systems with polytopic parameter uncertainty. We aim to derive a less-conservative design than existing linear matrix inequality (LMI) based sufficient conditions. It is shown that a more efficient evaluation of robust H2or 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 provide extra degrees of freedom in optimizing the guaranteed H2or H∞performance and lead to a less-conservative design.