On the stabilizability of plants with variable operating condition (Q2725130)

The authors consider the feedback stabilization of the uncertain plant NEWLINE\[NEWLINEG(s)={n(s) \over d(s)}NEWLINE\]NEWLINE where \(n(s)=\alpha n_1(s)+(1-\alpha) n_2(s)\), \(d(s)=\alpha d_1(s)+ (1-\alpha) d_2(s)n_i(s)/d_i(s)\) being coprime factorizations and \(0< \alpha<1\). The controller is taken as NEWLINE\[NEWLINEK(s)= {n_k(s)\over d_k(s)}NEWLINE\]NEWLINE where NEWLINE\[NEWLINEn_k={\beta \alpha\over (\beta-1)\alpha +1}n_{k_1}+ {1-\alpha\over (\beta-1) \alpha+1}n_{k_2}NEWLINE\]NEWLINE NEWLINE\[NEWLINEd_k={\beta \alpha\over (\beta-1) \alpha+1} d_{k_1}+ {1-\alpha\over (\beta-1) \alpha+1}d_{k_2}NEWLINE\]NEWLINE \(\beta> 0\) is a design parameter and \(n_{k_i}/d_{k_i}\) are the compensators corresponding to the cases \(\alpha=0\) and \(\alpha=1\) respectively. Solvability conditions for this problem are given.