In this paper, the authors present a linear matrix inequality (LMI) approac
h to the strictly positive real (SPR) synthesis problem: find an output fee
dback K such that the closed-loop system T(s) is SPR, The authors establish
that if no such constant output feedback K exists, then no dynamic output
feedback with a proper transfer matrix exists to make the closed-loop syste
m SPR.
The existence of K to guarantee the SPR property of the closed-loop system
is used to develop an adaptive control scheme that can stabilize any system
of arbitrary unknown order and unknown parameters.