scholarly journals Control of Discrete-Time Singularly Perturbed Systems via Static Output Feedback

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Dan Liu ◽  
Lei Liu ◽  
Ying Yang
Keyword(s):  
Discrete Time ◽  
Output Feedback ◽  
Perturbation Parameter ◽  
Singularly Perturbed ◽  
Static Output Feedback ◽  
Singularly Perturbed Systems ◽  
Closed Loop System ◽  
Perturbed Systems ◽  
Norm Bound ◽  
Static Output

This paper concentrates on control problems of discrete-time singularly perturbed systems via static output feedback. Two methods of designing an controller, which ensures that the resulting closed-loop system is asymptotically stable and meets a prescribed norm bound, are presented in terms of LMIs. Though based on the same matrix transformation, the two approaches are turned into different optimal problems. The first result is given by an -independent LMI, while the second result is related to . Furthermore, a stability upper bound of the singular perturbation parameter is obtained. The validity of the proposed two results is demonstrated by a numerical example.

scholarly journals Asynchronous Stabilization of Nonlinear Markov Jump Singularly Perturbed Systems via Fuzzy Static Output Feedback Control

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Baogang Ding ◽  
Tingting Ma ◽  
Xiaoxin Feng ◽  
Yueying Wang
Keyword(s):  
Feedback Control ◽  
Output Feedback ◽  
Output Feedback Control ◽  
Singularly Perturbed ◽  
Static Output Feedback ◽  
Singularly Perturbed Systems ◽  
Markov Jump ◽  
Perturbed Systems ◽  
Static Output Feedback Control ◽  
Static Output

This study focuses on the static output feedback control of nonlinear Markov jump singularly perturbed systems within the framework of Takagi–Sugeno fuzzy approximation. From a practical point of view, the phenomenon of asynchronous switching between the plant and the controller is considered and characterized by a finite piecewise-homogenous Markov process. Particularly, for facilitating the controller synthesis, the closed-loop system is transformed into a fuzzy Markov jump singularly perturbed descriptor system by adopting descriptor representation. In order to fully accommodate the system features, an appropriate stochastic Lyapunov function is constructed. Afterwards, by combining Finsler’s lemma, the mean square exponential admissibility of the system is analyzed. The conditions ensuring the existence of the predesigned controller are given and further solved by designing a brief search algorithm. Finally, a typical circuit system is used to demonstrate the application potential of the developed control technology and the effectiveness of the control strategy.

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.

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