Reduced-order controller design for the general H-infinity control problem

摘要

This paper considers reduced-order controller design for the general H-infinity control problem. Based on linear matrix inequality (LMI), two new upper bounds of order reduction are proposed in continuous- and discrete-time contexts respectively. The bounds have a clear geometric interpretation and are only determined by the generalized plant parameter matrices. Moreover, the existence conditions of the reduced-order controller have the same forms as the well-known three LMIs, but with fewer dimension matrix variables. In comparison with the previous results, one of the main advantages is that our approach is applicable to general H-infinity control. Furthermore, the existing results do not imply our results for singular H-infinity control. An illustrative example is given to show the efficiency of our approach.