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1

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.

2

Optimal control for bilinear systems with delay on control

Eljai A., Karrakchou J., Rachik M., Lhous M.

Archives of Control Sciences

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2001

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Vol. 11, no. 1/2

23-55

EN

The quadratic optimal control for bilinear distributed systems with delays in the control is considered. A semigroup model which involves no explicit delays in control is introduced. In the case of continuous delay, the control operator is bounded and the classical results can be applied. The case of general delays can be considered as a distributed system with boundary control. With the aid of a family of approximating systems, it is shown that the optimal control is obtained as a limit of sequence which is solution of classical control problems.

3

Linear Quadratic Control Problem With Fixed Final State for Discrete-Time Distributed Systems

Chraibi L., Karrakchou J., Ouansafi A., Rachik M.

International Journal of Applied Mathematics and Computer Science

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2000

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Vol. 10, no 3

517-535

EN

The problem considered is that of minimizing a quadratic cost functional for a discrete distributed system with fixed initial and final states. It is shown that under suitable controllability assumptions, there is a close relationship between this problem and that of exact controllability with minimization of a time-varying energy criterion. The HUM technique is then extended to treat the exact controllability problem in the time-varying case and applied to provide an explicit form for the optimal control and the optimal cost.

4

Spreadability and spray actuators

El Yacoubi S., El Jai A., Karrakchou J.

Applied Mathematics and Computer Science

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1998

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Vol. 8, no 2

367-379

EN

Spreadability of distributed systems has been recently introduced (El Jai and Kassara, 1994; El Jai et al., 1995). The aim of this paper is to propose a new approach to spreadability based on considering actuators as generators of spreadability. This approach is related to ecological and environmental problems, like vegetation dynamics, where the actuators are assumed to be governed by a transport equation while the system is described by a diffusion model.