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Robust pole assignment of uncertain discrete systems with input time-delay

A algorithm of proposed problem of robust pole assignment of uncertain discrete systems with input time-delay is given based on the eigenstructure assignment approach in discrete time-delay systems with state feedback and the analytic parameter solution to high-order Sylvester matrix equation. First the study focuses on the solution to eigenstructure assignment of the nominal system, complete parametric expressions of eigenvectors matrix and the state feedback controller are proposed. Then according to the chosen optimal index, a set of parameters of the robust pole assignment is given by optimizing the freedom degrees existing in the solution to eigenstructure assignment problem. Finally, the robustness state feedback controller is obtained, which ensures the minimum sensitivity of the closed-loop system with the uncertain parameters. An example with simulation illustrates the effect of the proposed algorithm.