Stabilization and robust <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si6.gif" display="inline" overflow="scroll"><mml:msub><mml:mrow><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math> control for sector-bounded switched nonlinear systems

Hajiahmadi, Mohammad; Schutter, Bart De; Hellendoorn, Hans

doi:10.1016/j.automatica.2014.08.015

Cited by 33 publications

(5 citation statements)

References 15 publications

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“…In which, the main consideration is arbitrary switching. [26][27][28][29][30][31] The state-dependent switching is also considered in References 32 and 33. Therefore, it is significant to develop a novel design scheme for switching law or controller to stabilize the switched Lurie systems.…”

Section: Introductionmentioning

confidence: 99%

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Absolute stabilization of switched Lurie systems with dwell time via dynamic output feedback

Zhao,

Sun

2024

Intl J Robust & Nonlinear

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In this article, we study the absolute stabilization of switched Lurie system via dynamic output feedback, where the nonlinearity is unknown and is restricted in a sector. In most works, the nonlinearity is assumed to be known exactly or is restricted in a bounded sector. Here, we consider the most general case with unbounded sector. With the help of switched time‐varying Lyapunov–Lurie function, a dynamic output feedback controller with time‐varying control gain is presented. On this basis, sufficient conditions for absolute stabilization are derived in the framework of mode‐dependent minimum dwell time and mode‐dependent range dwell time. It turns out that this time‐varying control strategy can solve the absolute stabilization of switched Lurie systems that all subsystems are not stabilizable. Moreover, the stability criteria in terms of linear matrix inequality we derived can be easily checked via Matlab toolbox. Finally, the effectiveness of presented methods is verified by several numerical examples.

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Section: Introductionmentioning

confidence: 99%

“…Recent years, there have been few reports on stabilization and stability problems for switched Lurie systems. In which, the main consideration is arbitrary switching 26–31 . The state‐dependent switching is also considered in References 32 and 33.…”

Section: Introductionmentioning

confidence: 99%

Absolute stabilization of switched Lurie systems with dwell time via dynamic output feedback

Zhao,

Sun

2024

Intl J Robust & Nonlinear

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“…In the work by Li and Meng, 24 the designation idea of infinity controller was used in the switched Lurie system. Based on the multiple Lyapunov functions, the stabilization and robust H ∞ control of the switched Lurie systems under average dwell time were studied in the work by Hajiahmadi et al 25 The L 2 -induced gain of discrete-time switched Lurie systems with saturated input was investigated in the work by Louis et al 26 Note that the above of the nonlinearities of switched Lurie systems are limited to a bounded sector region. For the switched Lurie system with sector-unbounded nonlinearity, the research on the H ∞ control problem still remains challenging.…”

Section: Introductionmentioning

confidence: 99%

H∞ control of switched Lurie systems with dwell time

Zhao,

Sun

2024

Proceedings of the Institution of Mechanical Engineers, Part I:

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This article deals with the [Formula: see text] control problems of switched Lurie systems. Our purpose is to design switching signals and state feedback controllers with time-varying control gains that make the closed-loop switched Lurie systems absolutely stable. Based on switched time-varying Lyapunov–Lurie function, time-varying controllers corresponding to two kinds of switching signals are proposed. On this basis, the control synthesis conditions are given. It is worth mentioning that our results can deal with the situation that all subsystems are not stabilizable. Finally, the obtained results are applied to a flexible joint robotic arm model with switchings of parameter values. Another simulation example of switched Lurie systems is considered to illustrate the validity of the presented approaches.

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“…A possible way to reduce the conservatism is to consider a specific class of nonlinear functions and derive conditions specific for that class taking the particular structure into account. For the class of sector‐bounded functions of the state we could mention the References 12‐16. However, the class of systems considered in the previous papers is not general, multiple nonlinearities are not covered and the switching rule is based on the availability of complete state information.…”

Section: Introductionmentioning

confidence: 99%

“…However, the class of systems considered in the previous papers is not general, multiple nonlinearities are not covered and the switching rule is based on the availability of complete state information. Moreover, Hajiahmadi et al 12 considers generic quadrant-wide sectors, Dezuo et al 13,14 take advantage of the systems knowledge to propose less conservative, yet robust, sectors, while Yang et al 15 generalizes for systems with all unstable modes and arbitrary positive and negative sector bounds. Meanwhile, Geromel et al 16 and Yang et al 17 limits their results to the stability analysis of Lur'e systems.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear feedback switching rule design for sector‐bounded switched systems

Lunardi

Dezuo

Trofino

2023

Intl J Robust & Nonlinear

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This article presents a robust switching rule design technique for a class of nonlinear and uncertain switched systems. The approach is based on a state transformation that allows for nonlinear state feedback. The results are given in terms of linear matrix inequality problems and they guarantee global asymptotic stability of the closed-loop system even if sliding modes occur on any switching surface. The class of systems considered is general enough to include multiple time varying sector-bounded nonlinearities associated with real-time changes in the operation point. The potential of the method is illustrated through photovoltaic systems, in which the nonlinear I-V characteristic of the modules is treated as a sector-bounded function. As the slope of the sectors depend on the environmental conditions, robust sectors containing the nonlinearities for any uncertain uniform operation condition are derived.

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Stabilization and robust H∞ control for sector-bounded switched nonlinear systems

Cited by 33 publications

References 15 publications

Absolute stabilization of switched Lurie systems with dwell time via dynamic output feedback

Absolute stabilization of switched Lurie systems with dwell time via dynamic output feedback

H∞ control of switched Lurie systems with dwell time

Nonlinear feedback switching rule design for sector‐bounded switched systems

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