New Results on Stability of Slowly Switched Systems: A Multiple Discontinuous Lyapunov Function Approach

Zhao, Xudong; Shi, Peng; Yin, Yunfei; Nguang, Sing Kiong

doi:10.1109/tac.2016.2614911

Cited by 301 publications

(145 citation statements)

References 26 publications

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“…Since the common Lyapunov function based controller design is essentially conservative [15], multiple Lyapunov function method is proposed. The switching stability can be ensured even if each subsystem has an individual Lyapunov function under certain conditions [22]. Dwell time method is emphasis on the critical switching time for system stability.…”

Section: Introductionmentioning

confidence: 99%

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Robust Switching Control and Subspace Identification for Flutter of Flexible Wing

Wang

2018

Shock and Vibration

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Active flutter suppression and subspace identification for a flexible wing model using micro fiber composite actuator were experimentally studied in a low speed wind tunnel. NACA0006 thin airfoil model was used for the experimental object to verify the performance of identification algorithm and designed controller. The equation of the fluid, vibration, and piezoelectric coupled motion was theoretically analyzed and experimentally identified under the open-loop and closed-loop condition by subspace method for controller design. A robust pole placement algorithm in terms of linear matrix inequality that accommodates the model uncertainty caused by identification deviation and flow speed variation was utilized to stabilize the divergent aeroelastic system. For further enlarging the flutter envelope, additional controllers were designed subject to the models beyond the flutter speed. Wind speed was measured online as the decision parameter of switching between the controllers. To ensure the stability of arbitrary switching, Common Lyapunov function method was applied to design the robust pole placement controllers for different models to ensure that the closed-loop system shared a common Lyapunov function. Wind tunnel result showed that the designed controllers could stabilize the time varying aeroelastic system over a wide range under arbitrary switching.

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Section: Introductionmentioning

confidence: 99%

“…It can be precisely computed based on exact dynamic model and the conservative of controller design is significantly decreased while the switching speed is less than dwell time. For slow switching system, several efficient methods are proposed based on dwell time theory [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Robust Switching Control and Subspace Identification for Flutter of Flexible Wing

Wang

2018

Shock and Vibration

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“…In recent 2 years, analysis of HSIS such as stability and stabilization analysis and controller design of HSIS has been studied so much as a hot topic among various research fields and many valuable results were obtained. Some of the works in recent 2 years are global stability for switched systems, noise‐to‐state stability of random switched systems, stability analysis and control design of switched affine systems, stability of switched nonlinear systems, dissipativity‐based filtering design for switched systems, observed‐based adaptive controller design, and predictive control of switched linear systems; for more results, see previous studies …”

Section: Introductionmentioning

confidence: 99%

On singular hybrid switched and impulsive systems

Zamani

Shafiee

Ibeas

2017

Intl J Robust & Nonlinear

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Summary In this work, the problem of stability analysis for a class of singular hybrid switched and impulsive system (HSIS) is addressed. Corresponding to each subsystem, a hybrid switched and impulsive controller is designed and then the exponential stability property of the proposed singular HSIS is discussed for linear and nonlinear cases. Because switched systems without impulses are a special case of HSISs, the results are also given to switched system with synchronous and asynchronous controllers. The obtained results apply to control singular systems, and the introduced theorems allow knowing how the control must be designed. Two numerical examples are given to show the effectiveness of the proposed approaches. At first, by using MATLAB® software, the proposed method is applied to a class of physiological processes of endocrine disruptor diethylstilbestrol models to illustrate the effectiveness of the results obtained here for the linear case. Thereafter, another numerical example is provided to support the presented theoretical results for the nonlinear case.

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“…If hybrid systems consist of a family of dynamical subsystems and a switching signal which determines the switching manner between the subsystems, they are called switched systems [9][10][11]. A system is positive if for any nonnegative initial condition its state variables and outputs naturally take non-negative values for all nonnegative times.…”

Section: Introductionmentioning

confidence: 99%

Input–Output Finite Time Stabilization of Time-Varying Impulsive Positive Hybrid Systems under MDADT

Yao

2017

Applied Sciences

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Time-varying impulsive positive hybrid systems based on finite state machines (FSMs) are considered in this paper, and the concept of input-output finite time stability (IO-FTS) is extended for this type of hybrid system. The IO-FTS analysis of the single linear time-varying system is given first. Then, the sufficient conditions of IO-FTS for hybrid systems are proposed via the mode-dependent average dwell time (MDADT) technique. Moreover, the output feedback controller which can stabilize the non-autonomous hybrid systems is derived, and the obtained results are presented in a linear programming form. Finally, a numerical example is provided to show the theoretical results.

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New Results on Stability of Slowly Switched Systems: A Multiple Discontinuous Lyapunov Function Approach

Cited by 301 publications

References 26 publications

Robust Switching Control and Subspace Identification for Flutter of Flexible Wing

Robust Switching Control and Subspace Identification for Flutter of Flexible Wing

On singular hybrid switched and impulsive systems

Input–Output Finite Time Stabilization of Time-Varying Impulsive Positive Hybrid Systems under MDADT

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