Design of a new interpolated controller for stabilization of a set of interpolated plants (Q2764369)

The authors consider a feedback control system composed of a controller and a plant \(G\), which is assumed to lie in the following set of interpolated models: NEWLINE\[NEWLINE\left\{\begin{aligned} G&=ND^{-1}\\ N&=\alpha\cdot N_1U_1 + (1 - \alpha)\cdot N_2U_2\\ D&=\alpha\cdot D_1U_1+ (1-\alpha)\cdot D_2U_2\end{aligned}\right.NEWLINE\]NEWLINE where \(\alpha\) \((0\leqslant\alpha\leqslant 1)\) is a parameter which represents the variation of the plant dynamics, \(U_1\), \(U_2\) are unknown, but they are unimodular matrices over \(RH_\infty\) and satisfy \(\|U_i-I \|_\infty\leqslant\delta\), where \(\delta \) \((0\leqslant\delta<1)\) is known. A new interpolated controller that is a linear interpolation of coprime factorizations of two stabilizing controllers for the two representative models is designed to stabilize this set of interpolated models for all \(\alpha\in [0,1]\). The design of such an interpolated controller is converted to a feasibility problem constrained by several LMIs and a BMI, and a two-step iteration algorithm is employed to solve it.