An LMI approach to H2/H∞ synthesis for polytopic uncertain systems

This paper deals with multi-objective output feedback synthesis for linear time invariant polytopic uncertain systems (LTI). Specifications and objectives addressed include H₂,and H_∞ performance. An LMI based approach is given to solve this problem. The LMI theory gives a necessary and sufficient condition for a mixed H₂ and H_∞ dynamic output control problem. This condition is bilinear with respect to the unknowns. However, efficient numerical procedures are likely to be developed. This procedure is based on a cross decomposition algorithm. Finally, the validity and applicability of this approach are illustrated by a benchmark example.