Application of Mathematics for Robust Stability and for Robustly Strictly Positive Real on an Uncertain Interval Plant

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.