Robust guaranteed cost control for uncertain linear differential systems of neutral type. (Q1406275)

The following differential system is considered: \[ \dot{x}(t)=A_{0}x(t)+A_{1}x(t-h)+ C\dot{x}(t-h)+f(t,x(t),x(t-h))+Bu(t), \] \[ x(t)=\varphi(t),\quad t\in[-h,0], \] with a feedback controller \[ u(t)=-B^{T}Px(t) \] and with the cost function \[ \int_{0}^{\infty}(x^{T}(t)Qx(t)+u^{T}(t)Su(t))\,dt. \] By the matrix inequality approach the author proves that the closed-loop system is robustly stable and that the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainty and time delay.