Pole placement for discrete-time systems via multiple parametric Lyapunov equations

This paper investigates the pole placement problem of discrete-time systems. To retain the advantages of the parametric discrete-time Lyapunov equation, matrix-partitioning idea is used to derive a new pole shift lemma. Starting from system matrix transformations, a recursive method that shifts every eigenvalue of a discrete-time system separately without mode decomposition in each step is proposed. Compared with existing methods, this one not only leads to analytical solutions to feedback gains but also may need low computation cost on flexible pole placement. As an application, the semiglobal stabilization with guaranteed flexible pole placement for saturated discrete-time systems is achieved using this method.

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