Robust H2 estimation and control

Abstract

This paper is concerned with the H2 estimation and control problems for uncertain discretetime systems with normbounded parameter uncertainty. We first present an analysis result on 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 terms 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 traditional Riccati equation approach since no separation principle has been known for uncertain systems. The design approach is demonstrated through a simple example.