Application of Mathematics for Robust Stability and for Robustly
Strictly Positive Real on an Uncertain Interval Plant
Abstract
In this paper, we present one Robust control Problem where
\mathcal{P}=\{P(s,l,m)=U(s,l)/V(s,m):l\in
L,m\in M \} is a family of interval
plants. Considering a multilinear function with two uncertain parameters
l and m, we have shown the strictly positive real (SPR) constructing
four Kharitonov Polynomials for that problem. For this case, the aim of
the paper is twofold. First, we approach to show the robust stability of
{P}(s,l,m). Second we show
that \displaystyle{\min_{l\in
L,m\in M}}~~{Re
U\left(j\omega,l
ight)V^\ast\left(j\omega,m
ight)>0} where
V^\ast\left(j\omega,m
ight) is conjugate of V(j\omega,m) and
s=j\omega where omega is frequency assuming some domain.
Then we have illustrated one example.
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