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Model reduction problem of linear discrete systems: Admissibles initial states

100%

Abdelhak A. , Rachik M. , Abdelhak A. , Rachik M.

Model reduction problem of linear discrete systems: Admissibles initial states

89%

Abdelhak A. , Rachik M.

Archives of Control Sciences

2019

tom Vol. 29, No. 1

41--55

Given a linear discrete system with initial state x0 and output function yi , we investigate a low dimensional linear system that produces, with a tolerance index ϵ, the same output function when the initial state belongs to a specified set, called ϵ-admissible set, that we characterize by a finite number of inequalities. We also give an algorithm which allows us to determine an ϵ-admissible set.

Optimizing the Linear Quadratic Minimum-Time Problem for Discrete Distributed Systems

89%

Rachik M. , Abdelhak A.

International Journal of Applied Mathematics and Computer Science

2002

tom Vol. 12, no 2

153-160

With reference to the work of Verriest and Lewis (1991) on continuous finite-dimensional systems, the linear quadratic minimum-time problem is considered for discrete distributed systems and discrete distributed time delay systems. We treat the problem in two variants, with fixed and free end points. We consider a cost functional J which includes time, energy and precision terms, and then we investigate the optimal pair (N,u) which minimizes J.

On the admissible perturbations for discrete systems

89%

Rachik M. , Abdelhak A.

Archives of Control Sciences

2002

tom Vol. 12, no. 3

301-313

We consider a discrete system described by xi+1=Axi, i>0 with the output function yi=Cxi, i>0 which is subject to the constraints (...). Then we investigate the admissible nonlinear perturbations (Ni)i, i.e., the ones such that the corresponding perturbed output function (...) remains in the constraints set omega for all i>0.