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1
Content available Ideal observability for bilinear discrete-time systems with and without delays in observation
Lhous M., Rachik M., Magri E. M.
Archives of Control Sciences
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2018
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Vol. 28, No. 4
601--616
EN
An ideal observability subspace expression is stated for bilinear abstract system with bounded operator in Hilbert spaces. The case of finite dimentional space is also treated. However, it’s noticed that the state ideal observability can never be fulfilled within an infinite dimensional phase space in the case of scalar output. The case of bilinear discrete-time system with delays in observation is also described. To illustrate this work some examples are presented.
2
Content available An observer-based control of linear systems with uncertain parameters
Rachik M., Lhous M.
Archives of Control Sciences
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2016
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Vol. 26, no. 4
565--576
EN
In this paper, the observer-based control for a class of uncertain linear systems is considered. Exponential stabilizability for the system is studied and reduced-order observer is discussed. Numerical examples are given to illustrate obtained results.
3
Content available remote A quadratic optimal control problem for a class of linear discrete distributed systems
Rachik M., Lhous M., El Kahlaoui O., Labriji E., Jourhmane H.
International Journal of Applied Mathematics and Computer Science
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2006
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Vol. 16, no 4
431-440
EN
A linear quadratic optimal control problem for a class of discrete distributed systems is analyzed. To solve this problem, we introduce an adequate topology and establish that optimal control can be determined though an inversion of the appropriate isomorphism. An example and a numerical approach are given.
4
Content available remote Admissible disturbances for perturbed nonlinear discrete systems
Rachik M., Tridane A., Lhous M., Tridane Z.
Archives of Control Sciences
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2006
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Vol. 16, no. 3
297-314
EN
Consider the discrete perturbed controlled nonlinear system given by { xe (i+1)=Axe(i) + f(ζiui+ωi), i≥0 xe(0)=γx0+ψ The disturbance e is said to be ε-admissible if IIye(i) - y(i)II ≤ε, ∀≥0. The set of all ε-admissible disturbances is the admissible set σ(ε). The characterization of σ(ε) is investigated and practical algorithms with numerical simulation are given. The admissible set σd(ε) for discrete delayed systems is also considered.
5
Content available remote 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.
6
Content available remote On the asymptotic stability of nonlinear discrete systems
Rachik M., Lhous M., Tridane A.
Archives of Control Sciences
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2000
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Vol. 10, no. 3/4
125-140
EN
Discrete nonlinear systems are considered. Inspired by what was done in (Banks et al., 1996) and (Hong et al., 1994), we develop some sufficient conditions which assure the stability of discrete-time nonlinear varying systems. The problem for discrete delayed systems is also considered.
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