scholarly journals Robust Observer-Based Feedback Control for Lipschitz Singularly Perturbed Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yanyan Wang ◽  
Wei Liu
Keyword(s):  
Feedback Control ◽  
Small Perturbation ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Linear Matrix ◽  
Observation Error ◽  
Singularly Perturbed Systems ◽  
Perturbed Systems ◽  
Exponentially Stable ◽  
The Stability

The observer-based feedback control for singularly perturbed systems (SPSs) with Lipschitz constraint is addressed. A sufficient condition, independent of the perturbation parameter, for a full-order observer is presented in terms of linear matrix inequality (LMI) such that observation error is exponentially stable for all sufficiently small perturbation parameters. Then, for observer-based feedback control, a proper controller is constructed to guarantee the input-to-state stability of the system with regard to the observation error. Considering the convergence of observation error, the stability of the system can be obtained based on the input-to-state stability property. It is shown that the proposed method is simple and easy to operate. Moreover, the upper bound of the small perturbation parameter for stability of systems can be explicitly estimated with a workable computation way. Finally, two numerical examples show the effectiveness of the proposed method.

scholarly journals On Guaranteed Global Exponential Stability Of Polynomial Singularly Perturbed Control Systems

2006 ◽  
Vol 1 (4) ◽  
pp. 21 ◽  
Author(s):  
Hajer Bouzaouache ◽  
Naceur Benhadj Braiek
Keyword(s):  
Exponential Stability ◽  
Global Exponential Stability ◽  
Integral Manifold ◽  
Singularly Perturbed ◽  
Linear Matrix ◽  
Singularly Perturbed Systems ◽  
Closed Loop System ◽  
Reduced Order ◽  
Perturbed Systems ◽  
The Stability

The problem of global exponential stability for a class of nonlinear singularly perturbed systems is examined in this paper. The stability analysis is based on the use of basic results of integral manifold of nonlinear singularly perturbed systems, the composite Lyapunov method and the notations and properties of Tensoriel algebra. Some of the derived results are presented as linear matrix inequalities (LMIs) feasibility tests. Moreover, we pointed out that if the global exponential stability of the reduced order subsystem is established this is equivalent to guarantee the global exponential stability of the original high order closed loop system. An upper bound e1 of the small parameter e , can also be determined up to which established stability conditions via LMI’s are maintained verified. A numerical example is given to illustrate the proposed approach.

Discrete-Time Nonlinear Singularly Perturbed System Identification Using Coupled Multimodel Representation

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Asma Ben Rajab ◽  
Nesrine Bahri ◽  
Majda Ltaief
Keyword(s):  
Discrete Time ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
System Model ◽  
Model Parameters ◽  
Singularly Perturbed Systems ◽  
Perturbed System ◽  
Marquardt Algorithm ◽  
Perturbed Systems ◽  
Full Knowledge

Abstract Many control and observability theories for singularly perturbed systems require the full knowledge of system model parameters exceptionally if the system is considered as black box. To overcome this problem and to obtain an accurate and faithful model, this paper describes a new identification method for discrete-time nonlinear singularly perturbed systems (NLSPS) using the coupled state multimodel representation. The Levenberg–Marquardt algorithm is used to identify not only the submodels parameters but also the perturbation parameter ε. Two cases are considered to identify these systems. The first one supposes that the perturbation parameter ε of the real system is known and thus only the submodels parameters are identified. The second case supposes that this perturbation parameter is unknown and has to be identified with the other submodels parameters. The simulation example demonstrates the effectiveness of the proposed identification.

Composite feedback control of discrete multiparameter singularly perturbed systems

1998 ◽  
Vol 69 (4) ◽  
pp. 577-597 ◽  
Author(s):  
Shing-Tai Pan ◽  
Feng-Hsiag Hsiao ◽  
Lin-Goei Hsiau
Keyword(s):  
Feedback Control ◽  
Singularly Perturbed ◽  
Singularly Perturbed Systems ◽  
Perturbed Systems

scholarly journals Diagnosis of Discrete-Time Singularly Perturbed Systems Based on Slow Subsystem

2014 ◽  
Vol 8 (4) ◽  
pp. 175-180 ◽  
Author(s):  
Adel Tellili ◽  
Nouceyba Abdelkrim ◽  
Bahaa Jaouadi ◽  
Mohamed Naceur Abdelkrim
Keyword(s):  
Discrete Time ◽  
Diagnostic Algorithm ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Order System ◽  
Singularly Perturbed Systems ◽  
Perturbed Systems ◽  
Parity Space ◽  
The One ◽  
Slow Subsystem

Abstract This paper deals with the diagnosis of discrete-time singularly perturbed systems presenting two time scales property. Parity space method is considered to generate the fault detection residual. The focus is in two directions. First, we discuss the residual illconditioning caused by the singular perturbation parameter. Then, the use of the slow subsystem is considered to make the fault diagnosis easier. It is shown that the designed diagnostic algorithm based on reduced order model is close to the one synthesized using the full order system. The developed approach aims at reducing the computational load and the ill-conditioning for stiff residual generation problem. Two examples of application are used to demonstrate the efficiency of the proposed method.

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