Robust H2 estimation and control

This paper is concerned with the H₂ estimation and control problems for uncertain discrete-time systems. We first present an analysis result of H₂ norm bound for a stable uncertain system in terms of linear matrix inequalities (LMIs). A solution to the robust H₂ estimation problem is then derived in term of two LMIs. As compared to the existing results, our result on robust H₂ estimation is more general. In addition, explicit search of appropriate scaling parameters is not needed as the optimization is convex in the scaling parameters. The LMI approach is also extended to solve the robust H₂ control problem which has been difficult for the tradition Riccati equation approach since no separation principle has been known for uncertain systems. The design approach is demonstrated through a simple example of target tracking.