R. Bouyekhf

Bio: R. Bouyekhf is an academic researcher from École Normale Supérieure. The author has contributed to research in topics: Nonlinear system & Singular perturbation. The author has an hindex of 4, co-authored 4 publications receiving 50 citations.

On analysis of discrete singularly perturbed non-linear systems: Application to the study of stability properties

Abstract: Recently we have introduced a model of singular perturbation for discrete-time non-linear systems. This paper is aimed at validating the proposed model. In fact, a discrete version of the well-known Tikhonov's theorem on singular perturbation of continuous-time systems is established. The second aim is to study stability problems of such systems. Sufficient conditions for both asymptotic and exponential stability are obtained. As a result, significant order reduction of stability problems is achieved. This is achieved by allowing a small parameter whose upper bound is estimated. Finally a simple example is given to illustrate the applications of the results.

Reduced order modelling of two-time-scale discrete non-linear systems

Abstract: Application of two-time scale discrete singular perturbation methods have been limited to the linear systems. The area of discrete-time non-linear systems has received little attention. This paper deals with the singular perturbation model of non-linear discrete-time dynamic systems. We present a specific modelling and a mode decoupling approach well adapted for such systems. A comparison principle is used for grouping slow and fast states of a class of non-linear discrete systems. Finally, an example is given to show the feasibility of the theoretical results.

Stabilization and regulation of class of non-linear singularly perturbed discrete-time systems

Abstract: A class of discrete-time nonlinear systems which are two-time-scale is treated. Using the singular perturbation theory in a systematic way, we present a mode-decoupling approach which yields two separate subsystems containing the slow and fast parts. Furthermore, a two-time-scale analysis and design procedure for stabilization and regulation is presented. The controllability and stabilizability invariance of the fast subsystem is shown and an asymptotic stabilizing composite feedback control is proposed. Finally, it is shown that the composite control produces a finite cost which tends to the optimal cost of a slow problem as the singular perturbation parameter tends to zero.

Singular perturbations and time scales in control theory and applications: An overview

Abstract: This paper presents an overview of singular perturbations and time scales (SPaTS) in control theory and applications during the period 1984-2001 (the last such overviews were provided by [231, 371]). Due to the limitations on space, this is in way intended to be an exhaustive survey on the topic.

Optimal control of a particular class of singularly perturbed nonlinear discrete-time systems

Abstract: This note studies a class of discrete-time nonlinear systems which depend on a small parameter. Using the singular perturbation theory in a systematic way, we give a trajectory approximation result based on the decomposition of the model into reduced and boundary layer models. This decomposition is used to analyze optimal control via maximum principle of such systems. As a result, significant order reduction of optimal control problems is achieved.

On analysis of discrete singularly perturbed non-linear systems: Application to the study of stability properties

Abstract: Recently we have introduced a model of singular perturbation for discrete-time non-linear systems. This paper is aimed at validating the proposed model. In fact, a discrete version of the well-known Tikhonov's theorem on singular perturbation of continuous-time systems is established. The second aim is to study stability problems of such systems. Sufficient conditions for both asymptotic and exponential stability are obtained. As a result, significant order reduction of stability problems is achieved. This is achieved by allowing a small parameter whose upper bound is estimated. Finally a simple example is given to illustrate the applications of the results.

Discrete singularly perturbed control problems (A survey)

Abstract: The paper presents the review of various types of discrete singularly perturbed control problems and methods for solving them. The bibliography containing 157 titles is included.

Stability Analysis of Nonstandard Nonlinear Singularly Perturbed Discrete Systems

Abstract: In this brief, we consider the stability problem of nonstandard nonlinear singularly perturbed discrete systems (NN-SPDSs). Specifically, an NN-SPDS is decomposed into two standard nonlinear SPDSs. Based on the lower order subsystems of the standard nonlinear SPDSs, we analyze the stability of the NN-SPDS.