Robust passive control for linear systems with norm-bounded time-varying uncertainty

This paper concerns the robust passive control problem for linear systems with norm-bounded time-varying uncertainties in all the system matrices. Our objective is to design a feedback controller such that the closed-loop system is both quadratically stable and strictly passive for all admissible uncertainties. It is shown that such a problem is equivalent to a scaled strictly positive real control problem for a certain linear time-invariant system in which no uncertainty occurs. Therefore, a complete solution can be obtained by using the existing results of standard positive real control.