Robust passive control for singular systems with time-varying uncertainties

The problem of designing robust passive controllers is addressed for a singular system in which all coefficient matrices except E contain norm_bounded time_varying uncertainties. Using the method of linear matrix inequality (LMI), a sufficient condition was firstly presented for the unforced system to be generalized quadratically stable and passive. Then the existence condition of a state feedback robust passive controller was given and the explicit expression of the controller was derived in terms of the solution of LMIs. Furthermore, the existence condition of a dynamic output feedback robust passive controller was shown by means of matrix inequalities, and the design method of the controller was also given via solving matrix inequalities. Finally, an example was given to illustrate the validity of the proposed methods.