Comments on "Asymptotic stability for a class of linear discrete systems with bounded uncertainties" [with reply]

Corless, Martin; Mahmoud, Magdi S.; Bahnasawi, Ahmed A.

doi:10.1109/9.50366

Cited by 6 publications

(3 citation statements)

References 4 publications

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“…Generally, the uncertainty is employed to represent the inaccurate parameters and described via a time-varying function. In the literatures [1][2][3][4][5][6][7][8][9], the robust control methods have been proposed to design the controller such that stability of uncertain systems is guaranteed. Among of the literatures [1][2][3], the uncertainty is constructed via specific function to simulate the parameters varying.…”

Section: Introductionmentioning

confidence: 99%

Gain-scheduled controller design for discrete-time Linear Parameter Varying systems with multiplicative noises

Chen

2015

Int. J. Control Autom. Syst.

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In this paper, two technologies to design gain-scheduled controller are proposed for discretetime Linear Parameter Varying (LPV) systems with multiplicative noises. In the considered systems, the time-varying parameters are proposed to describe the uncertainties. And, the added multiplicative noise term is applied to describe the stochastic behaviors of the system. Furthermore, the gainscheduled design scheme is applied to deal with the stabilization problem of the LPV systems with multiplicative noises. Through the parameter-independent and parameter-dependent Lyapunov functions, the corresponding sufficient conditions are derived to discuss the stability and stabilization problems of the system. In order to apply the convex optimization algorithm, the derived sufficient conditions are converted into Linear Matrix Inequality (LMI) problems. Based on the proposed design technologies, gain-scheduled controllers are designed such that the considered system is asymptotically stable in the mean square. Finally, two numerical examples are applied to demonstrate the application and effectiveness of the proposed design technologies of this paper.

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Section: Introductionmentioning

confidence: 99%

Gain-scheduled controller design for discrete-time Linear Parameter Varying systems with multiplicative noises

Chen

2015

Int. J. Control Autom. Syst.

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“…Unfortunately, the accurate parameters are hardly to be obtained in practical applications due to modeling errors and natural perturbations. For this reason, robust control schemes [1][2][3][4][5][6][7][8][9][10][11][12] were proposed to guarantee stability of dynamic system with admissible uncertainties. Through [1][2][3], the uncertainty of system is described by norm bounded time-varying function.…”

Section: Introductionmentioning

confidence: 99%

“…For this reason, robust control schemes [1][2][3][4][5][6][7][8][9][10][11][12] were proposed to guarantee stability of dynamic system with admissible uncertainties. Through [1][2][3], the uncertainty of system is described by norm bounded time-varying function. On the other hand, based on LPV modeling approach [4][5][6], the uncertain systems can be interpreted by combining several subsystems and chosen time-varying weighting function.…”

Section: Introductionmentioning

confidence: 99%

H∞Gain-Scheduled Control for LPV Stochastic Systems

Chen

2015

Mathematical Problems in Engineering

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A robust control problem for discrete-time uncertain stochastic systems is discussed via gain-scheduled control scheme subject toH∞attenuation performance. Applying Linear Parameter Varying (LPV) modeling approach and stochastic difference equation, the uncertain stochastic systems can be described by combining time-varying weighting function and linear systems with multiplicative noise terms. Due to the consideration of stochastic behavior, the stability in the sense of mean square is applied for the system. Furthermore, two kinds of Lyapunov functions are employed to derive their corresponding sufficient conditions to solve the stabilization problems of this paper. In order to use convex optimization algorithm, the derived conditions are converted into Linear Matrix Inequality (LMI) form. Via solving those conditions, the gain-scheduled controller can be established such that the robust asymptotical stability andH∞performance of the disturbed uncertain stochastic system can be achieved in the sense of mean square. Finally, two numerical examples are applied to demonstrate the effectiveness and applicability of the proposed design method.

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Deterministic control of uncertain systems via a constructive use of Lyapunov stability theory

Leitmann

System Modelling and Optimization

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Comments on "Asymptotic stability for a class of linear discrete systems with bounded uncertainties" [with reply]

Cited by 6 publications

References 4 publications

Gain-scheduled controller design for discrete-time Linear Parameter Varying systems with multiplicative noises

Gain-scheduled controller design for discrete-time Linear Parameter Varying systems with multiplicative noises

H∞Gain-Scheduled Control for LPV Stochastic Systems

Deterministic control of uncertain systems via a constructive use of Lyapunov stability theory

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