Output feedback stabilization of uncertain dynamical systems

Given an uncertain dynamical system with a linear nominal part, matched uncertainties, and a measured output, a sufficient condition is given for the existence of an output feedback stabilizing controller. For the general multiinput multioutput case, checking the sufficient condition involves the selection of a matrix <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</tex> . For the special class of single input single output systems, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">F</tex> is a positive or negative scalar and it is shown that if the nominal system transfer function is strictly positive real, then an output feedback stabilizing controller does indeed exist.