Delay-dependent robust stability and control for jump linear systems with delays

Wu, Jian; Chen, Tongwen; Wang, Long

doi:10.1016/j.sysconle.2006.06.006

Cited by 91 publications

(87 citation statements)

References 21 publications

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“…The paper [24] extends some of the robust stability results of the class of linear discretetime systems with time-varying delays. The class of Markovian jump systems is an important family of systems subject to abrupt variations.…”

Section: Introductionmentioning

confidence: 71%

Robust H ∞ Control for Class of Discrete-Time Markovian Jump Systems with Time-Varying Delays Based on Delta Operator

Qiu

Yang

Shi

et al. 2008

Circuits Syst Signal Process

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In this paper, the problem of robust H ∞ state feedback control using a delta operator approach for a class of linear fractional uncertain jump systems with timevarying delays is investigated. Based on the Lyapunov-Krasovskii functional in the delta domain, a new delay-dependent H ∞ state feedback controller which requires both robust stability and a prescribed H ∞ performance is presented in terms of linear matrix inequalities. The sampling period T appears as an explicit parameter; therefore, it is easy to observe and analyze the effect of the results with different sampling periods. Furthermore, the proposed method can unify some previous related continuous and discrete systems into the framework of delta operator systems. Numerical examples are presented to illustrate the effectiveness of the developed techniques.

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Section: Introductionmentioning

confidence: 71%

Robust H ∞ Control for Class of Discrete-Time Markovian Jump Systems with Time-Varying Delays Based on Delta Operator

Qiu

Yang

Shi

et al. 2008

Circuits Syst Signal Process

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“…On the basis of a rough and preliminary literature overview it can be stated that the Linear Systems [54], [55], [56], and within this class the Positive Linear Systems [57] form a particular problem class that was well tackled on the basis of the generalization/extension of Lyapunov's method (namely the use of the Lyapunov-Krasovskii functional) [58], [59]. An important class is in which the time-delay itself is not constant [60].…”

Section: B the Prevailing Solutions According To The Current Literaturementioning

confidence: 99%

“…An important class is in which the time-delay itself is not constant [60]. Other approaches connect they results to the concept of "robust stability" [61], [62], [55], [63].…”

Section: B the Prevailing Solutions According To The Current Literaturementioning

confidence: 99%

Preliminary investigations on the applicability of the fixed point transformations-based adaptive control for time-delayed systems

Csanadi

Haidegger²,

Redjimi

et al. 2016

2016 IEEE 20th Jubilee International Conference on Intelligent Engineering Systems (INES)

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Abstract-In this paper, for the first time, a possible tackling of the problem of known time-delay by the use of a Fixed Point Transformation-based adaptive controller is investigated. This approach at first transform the control task into a fixed point problem then solves it via iteration. The preliminary results that were obtained by numerical simulations for a strongly nonlinear controlled system, a van der Pol oscillator, are promising. It is expedient to make further, systematic investigations.

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“…Then, by different model transformations, the less conservative results of H ∞ performance criteria for the Markovian jump linear systems with constant delay were presented in [12][13][14]. In [15], by using some zero equations, neither model transformation nor bounding technique for cross terms was required to obtain the delay-dependent results. However, to the authors' knowledge, the delay-dependent results of H ∞ performance criteria for Markovian jump systems with time-varying delays are fewer (the results for Markovian jump systems with interval time-varying delays are much fewer).…”

Section: Introductionmentioning

confidence: 99%

Delay‐dependent H_∞ performance analysis and filtering for Markovian jump systems with interval time‐varying delays

Zhao

Zeng

2010

Adaptive Control & Signal

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This paper investigates the problems of H ∞ disturbance attenuation and H ∞ filtering for Markovian jump systems with interval time-varying delays. In terms of linear matrix inequalities, a less conservative delay-range-dependent H ∞ performance condition for Markovian jump systems is proposed by constructing a different Lyapunov-Krasovskii functional. The resulting criterion has advantages over some previous ones in that they involve fewer matrix variables, but has less conservatism. Based on this new condition, an improved H ∞ filtering algorithm is developed. Numerical examples are provided to demonstrate the efficiency and reduced conservatism of the results in this paper.

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Delay-dependent robust stability and control for jump linear systems with delays

Cited by 91 publications

References 21 publications

Robust H ∞ Control for Class of Discrete-Time Markovian Jump Systems with Time-Varying Delays Based on Delta Operator

Robust H ∞ Control for Class of Discrete-Time Markovian Jump Systems with Time-Varying Delays Based on Delta Operator

Preliminary investigations on the applicability of the fixed point transformations-based adaptive control for time-delayed systems

Delay‐dependent H_∞ performance analysis and filtering for Markovian jump systems with interval time‐varying delays

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Delay-dependent robust stability and control for jump linear systems with delays

Cited by 91 publications

References 21 publications

Robust H ∞ Control for Class of Discrete-Time Markovian Jump Systems with Time-Varying Delays Based on Delta Operator

Robust H ∞ Control for Class of Discrete-Time Markovian Jump Systems with Time-Varying Delays Based on Delta Operator

Preliminary investigations on the applicability of the fixed point transformations-based adaptive control for time-delayed systems

Delay‐dependent H∞ performance analysis and filtering for Markovian jump systems with interval time‐varying delays

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Delay‐dependent H_∞ performance analysis and filtering for Markovian jump systems with interval time‐varying delays