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1 Archives of Control Sciences

1 2004

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On state and output stabilization of discrete delay systems

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Karrakchou J. , Namir A. , Lahmidi F. , Daafi B.

tom Vol. 14, no. 3/4

287-298

The problem of the state and output stabilization of discrete-time delay systems on Hilbert spaces is considered. Sufficient and necessary conditions for the state stabilization are given. Analogue results for the output stabilization are presented. This work is organized in three sections. The state stabilization problem is examined in section 2. The three principle notions of stability and stabilizability (uniform, strong and weak) are investigated. Using the state space technique, it is shown that this problem can be tackled considering an equivalent non delayed system. Sufficient and necessary conditions for the stabilization of the new system are then established. Using these results and similar methods, sufficient and necessary conditions for the output stabilization are developed in section 3. To illustrate this work, some examples are given.