Interpolation With Strictly ${\boldsymbol{F}}$-Positive Real Matrix and Application to Strong Stabilization

The necessary and sufficient conditions for the newly introduced problem to find a strictly
${\boldsymbol{F}}$
-positive real (S
${\boldsymbol{F}}$
-PR) interpolant for a one-sided rational interpolation are given, as well as the set of all solutions. The S
${\boldsymbol{F}}$
-PR property of the interpolant
${\boldsymbol{H}}$
, for a rational matrix (RM)
${\boldsymbol{F}}$
to be found, implies that
${\boldsymbol{H}}$
is bistable and biproper (BiPS). Since such an interpolant is needed in the strong stabilization problem, the interpolation result is used to develop a control design algorithm such that a stable stabilizing controller of degree
$n+\ell$
is constructed using the RMs
${\boldsymbol{F}}$
and
${\boldsymbol{H}}$
, where
$\ell$
is the number of unstable plant zeros. Examples, including one with a chemical reactor plant, illustrate the control design algorithm.