# zbMATH — the first resource for mathematics

Robust static output feedback control for discrete time-delay systems. (English) Zbl 1122.93027
Consider the discrete system $$x_{k+1} = A_0x_k + A_1x_{k-d} + Bu_k + Fw_k$$, $$y_k = Cx_k$$, $$z_k = Dx_k + Ew_k$$, where $$x_k$$, $$u_k$$, $$w_k$$, $$y_k$$ and $$z_k$$ are the state, control, disturbance, measured output and controlled output vectors, respectively. The delay $$d$$ is unknown and the matrix coefficients $$A_0,A_1,\dots,E$$ contain uncertainties represented by a convex bounded polytopic model. The control is chosen as $$u_k = Ly_k$$. Expressions for the gain matrix $$L$$ are derived which ensure (i) robust stabilization and (ii) robust $$H_\infty$$ performance of the closed-loop system $$x_{k+1} = (A + BLC)x_k + A_1x_{k-d} + Fw_k$$, $$z_k = Dx_k + Ew_k$$.

##### MSC:
 93B35 Sensitivity (robustness) 93B36 $$H^\infty$$-control 93B52 Feedback control 93C55 Discrete-time control/observation systems