An extension of estimation of domain of attraction for fractional order linear system subject to saturation control

Shahri, Esmat Sadat Alaviyan; Alfi, Alireza; Machado, J. A. Tenreiro

doi:10.1016/j.aml.2015.02.020

Cited by 42 publications

(2 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There may be many ellipsoids that satisfy the invariant set condition in Theorem 1, we would like to choose the “largest” one from among them to maximize the estimation of domain of attraction. In the literature (e.g., see References 2,30,31), the largeness of a set is usually measured by its volume or shape. Here, we maximize the estimation of the domain of attraction for the closed‐loop system () by taking the shape of a set into consideration.…”

Section: Estimation Of Domain Of Attractionmentioning

confidence: 99%

Robust exponential stabilization and L₂‐gain analysis for saturated switched nonlinear systems subject to actuator failure under asynchronous switching

Chen,

Zhang

2023

Optim Control Appl Methods

View full text Add to dashboard Cite

For the nonlinear continuous‐time switched system with input saturation under asynchronous switching action, the problem of actuator failure is investigated in the presence of external disturbances. Firstly, a sufficient condition for the robust exponential stabilization of system is obtained by using the minimum dwell‐time method combining the piecewise Lyapunov function method. Secondly, a sufficient condition for the tolerance disturbances of the system is obtained by using the similar approach. Thirdly, the weighted ‐gain is analysed. Then, we maximize the estimation of the domain of attraction for the closed‐loop system by taking the shape of a set into consideration. Furthermore, the fault‐tolerant state feedback controllers are designed, which aim at enlarging the estimation of domain of attraction for the closed‐loop system and obtaining the maximum value of tolerance disturbance and the minimum upper bound on the weighted ‐gain. Last but not least, we give a numerical example to verify the effectiveness of the proposed approach and compare the state responses curve under the action of the fault‐tolerant and the standard controller.

show abstract

Section: Estimation Of Domain Of Attractionmentioning

confidence: 99%

Robust exponential stabilization and L₂‐gain analysis for saturated switched nonlinear systems subject to actuator failure under asynchronous switching

Chen,

Zhang

2023

Optim Control Appl Methods

View full text Add to dashboard Cite

show abstract

“…In studies by Lim et al. (2013), Alaviyan Shahri et al. (2015), and Alaviyan Shahri and Balochian (2015a, 2016), the stability conditions of such systems were provided using the state feedback controller.…”

Section: Introductionmentioning

confidence: 99%

Robust stability and stabilization of uncertain fractional order systems subject to input saturation

Shahri

Alfi

Machado

2017

Journal of Vibration and Control

Self Cite

View full text Add to dashboard Cite

show abstract

Stability analysis of a class of nonlinear fractional‐order systems under control input saturation

Shahri

Alfi

Machado

2018

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

This paper studies the stability of a class of nonlinear fractional-order (FO) systems under input control saturation. Based on the Gronwall-Bellman lemma and the sector-bounded condition, sufficient conditions are provided to stabilize such systems by means of a state-feedback controller. The performance of the proposed controller is tested with 2 FO chaotic systems, namely, the FO brushless direct-current motor and the Chen systems. The results illustrate the good performance of the new controller under saturation effects. KEYWORDSchaotic system, fractional-order system, Gronwall-Bellman lemma, input saturation, sectorbounded condition INTRODUCTIONFractional-order (FO) systems have been studied in the past 2 decades for describing long memory and hereditary attributes of complex phenomena in different fields, such as energy fuels, 1 imaging science, 2 biomedicine 3 and accident analysis. 4 Therefore, the stability analysis of FO systems attracted considerable attention 5 and several results were reported in the literature addressing this topic. [6][7][8][9][10][11] Due to the simplicity in its design, most of the systems to be controlled are modeled in the perspective of linear dynamics. However, many physical phenomena involve nonlinear relationships between the variables, and there is a model mismatch between the real and the nominal models. Consequently, the stability problem of FO nonlinear dynamics represents an interesting and challenging topic. 12 In general, 2 techniques are addressed in the literature to study the stability of FO systems. The first is the FO extension of Lyapunov direct technique. [13][14][15][16][17][18] However, the use of this approach is often difficult because deriving Lyapunov functions is more complex for the FO case than for integer-order models. The second technique is based on solving or estimating the solution of models without considering control input saturation. [19][20][21] These methods allow some conclusions about stability, asymptotic stability, and Mittag-Leffler stability of FO systems but have the limitations referred previously.Both actuator and control input saturations are important issues in real-world control systems because actuators cannot provide unlimited efforts. Controllers that ignore the actuator saturation may cause undesirable responses and even closed-loop instability. 22 Therefore, it is important to compensate or at least to smoothen the saturation effects and to consider these options in the control design of FO systems. The stability analysis of FO systems under saturation has already received some attention. 14,15,[23][24][25] In related works, 14,15,23,24 simple models involving merely linear dynamics were used to study the stability of such systems, whereas the domain of attraction of the resultant closed-loop system subject to saturation was estimated by different techniques. In the work of Shahri et al, 25 a robust FO dynamic output-feedback sliding-mode controller was designed for a class of uncertain nonlinear FO systems under forced satu...

show abstract

An extension of estimation of domain of attraction for fractional order linear system subject to saturation control

Cited by 42 publications

References 15 publications

Robust exponential stabilization and L₂‐gain analysis for saturated switched nonlinear systems subject to actuator failure under asynchronous switching

Robust exponential stabilization and L₂‐gain analysis for saturated switched nonlinear systems subject to actuator failure under asynchronous switching

Robust stability and stabilization of uncertain fractional order systems subject to input saturation

Stability analysis of a class of nonlinear fractional‐order systems under control input saturation

Contact Info

Product

Resources

About

An extension of estimation of domain of attraction for fractional order linear system subject to saturation control

Cited by 42 publications

References 15 publications

Robust exponential stabilization and L2‐gain analysis for saturated switched nonlinear systems subject to actuator failure under asynchronous switching

Robust exponential stabilization and L2‐gain analysis for saturated switched nonlinear systems subject to actuator failure under asynchronous switching

Robust stability and stabilization of uncertain fractional order systems subject to input saturation

Stability analysis of a class of nonlinear fractional‐order systems under control input saturation

Contact Info

Product

Resources

About

Robust exponential stabilization and L₂‐gain analysis for saturated switched nonlinear systems subject to actuator failure under asynchronous switching

Robust exponential stabilization and L₂‐gain analysis for saturated switched nonlinear systems subject to actuator failure under asynchronous switching