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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 \(x_{k+1} = (A + BLC)x_k + A_1x_{k-d} + Fw_k\), \(z_k = Dx_k + Ew_k\).

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