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1

State estimation for nonlinear discrete-time delay systems

Labriji El H., Lahmidi F., Namir A.

Archives of Control Sciences

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2006

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Vol. 16, no. 4

463-473

2

On state and output stabilization of discrete delay systems

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

Archives of Control Sciences

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2004

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Vol. 14, no. 3/4

287-298

EN

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.

3

Detection and Control Problems for Non-Linear Distributed-Parameter Systems With Delays

Namir A., Lahmidi F., Labriji E. H.

International Journal of Applied Mathematics and Computer Science

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2000

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Vol. 10, no 3

437-464

EN

First, we consider non-linear discrete-time and continuous-time systems with unknown inputs. The problem of reconstructing an input using the information given by an output equation is investigated. Then we examine a control problem for non-linear discrete-time hereditary systems, i.e. the problem of finding a control which drives the state of the system from its initial value to a given desired final state. The methods used to solve these problems are based on the state-space technique and fixed-point theorems. To illustrate the outlined ideas, various numerical simulation results are presented.

4

Detection and Regulation Problems for Discrete-Time Distributed Systems With Delays

Namir A., Lahmidi F., Alif O.

International Journal of Applied Mathematics and Computer Science

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1999

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Vol. 9, no 2

347-369

EN

A distributed discrete-time hereditary system is considered. An unknown input is supposed to be a perturbation. First, we investigate the possibility of reconstructing this input using the information provided by an output equation. Then we treat the problem of keeping the observation as close as possible to some desired values (with the system still perturbed by the unknown input). To illustrate the results, some examples are presented.