On the design of nonfragile guaranteed cost controller for a class of uncertain dynamic systems with state delays.
The following controlled system is considered \[ \begin{multlined} \dot{x}(t)=A_{0}x(t)+\sum_{k=1}^{r}A_{k}x(t-h_{k}(t))+\Delta F_{x}(t,x(t)),x(t-h_{1}(t)),\dots,x(t-h_{k}(t))+\\ Bu(t)+\Delta F_{u}(t,u(t)),\quad t \in [0,\infty],\;x(t)=\theta(t),\;t \in [-H,0],\end{multlined} \] with a feedback controller \[ u(t)=-Kx(t) \] and with the cost function \[ \int_{0}^{\infty}(x^{T}(t)Qx(t)+u^{T}(t)Su(t))\,dt. \] Here \(\Delta F_{x}\) and \(\Delta F_{u}\) are unknown perturbations with conditions \[ \| \Delta F(t,z_{0},\dots,z_{r})\| \leqslant \sum_{k=0}^{r}\alpha_{k}\| z_{k}\| ,\| \Delta F(t,z)\| \leqslant \beta \| z\| ; \] \(0\leqslant h_{k}(t)\leqslant h_{k}<\infty,\dot{h}_{k}(t)\leqslant h_{2k}<1,H=(h_1,\dots,h_r).\) Under LMI conditions, the authors prove that closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound of a given cost function.
scientific article; zbMATH DE number 2056343