\(H_\infty\) control of discrete-time linear systems with time-varying delays in state
This paper is concerned with the \(H_\infty\) control of discrete-time linear systems with time-varying delays. The main result shows that if the system \[ \begin{aligned} x_{k+1} & = A_1x_k+ B_1u_k+ [A_2Q^{-1/2} \gamma^{-1} B_2]w_k,\\ z_k & = \Biggl[\begin{matrix} \sqrt mQ^{-1/2}\\ C\end{matrix}\Biggr] x_k+ \Biggl[\begin{matrix} 0\\ D\end{matrix}\Biggr] u_k\end{aligned} \] is quadratically stabilizable with a unitary \(H_\infty\) norm-bound, then the system \[ \begin{aligned} x_{k+1} & = A_1 x_k+ B_1 u_k+ B_2w_k,\\ z_k & = Cx_k+ Du_k\end{aligned} \] is stabilizable with an \(H_\infty\) norm-bound \(\gamma\) by the same control law. The proof is based on fairly standard linear matrix inequalities and Lyapunov theory.
scientific article; zbMATH DE number 1353728