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The robust stabilization problem for uncertain discrete singular time‐delay systems is addressed in this paper. In terms of strict linear matrix inequality and a finite sum inequality, a delay‐dependent criterion for the nominal systems to be admissible is obtained. Based on the criterion, a state feedback controller, which guarantees that, for all admissible uncertainties, the resulting closed‐loop system is regular, causal and stable, is constructed. An explicit expression for the desired controller is also given. The obtained results include both delay‐independent and delay‐dependent cases. Some numerical examples are introduced to show the effectiveness of the given results. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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Yuanqing Xia Author Vitae El-Kebir Boukas Author Vitae Jinhui Zhang Author Vitae 《Automatica》2009,45(6):1504-5640
In this paper, the problems of stability and state feedback stabilization for a class of continuous-time singular hybrid systems are investigated. A new sufficient and necessary condition for a continuous-time singular hybrid system to be regular, impulse-free and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities (LMIs). Moreover, a new sufficient and necessary condition is presented for the existence of the state feedback controller in terms of a set of coupled strict matrix inequalities. Finally, a numerical example is given to illustrate the effectiveness of the obtained theoretical results. 相似文献
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The problems of stability, state feedback control and static output feedback control for a class of discrete-time singular hybrid systems are investigated in this paper. A new sufficient and necessary condition for a class of discrete-time singular hybrid systems to be regular, causal and stochastically stable is proposed in terms of a set of coupled strict linear matrix inequalities (LMIs). Sufficient conditions are proposed for the existence of state feedback controller and static output feedback controller in terms of a set of coupled strict LMIs, respectively. Finally, two illustrative examples are provided to demonstrate the applicability of the proposed approach. 相似文献
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Delay-dependent stability analysis for Markovian jump systems with interval time-varying-delays 总被引:1,自引:0,他引:1
This paper proposes improved stochastic stability conditions for Markovian jump systems with interval time-varying delays. In terms of linear matrix inequalities (LMIs), less conservative delay-range-dependent stability conditions for Markovian jump systems are proposed by constructing a different Lyapunov-Krasovskii function. The resulting criteria have advantages over some previous ones in that they involve fewer matrix variables but have less conservatism. Numerical examples are provided to demonstrate the efficiency and reduced conservatism of the results in this paper. 相似文献
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This paper considers a dynamic output‐feedback control for continuous‐time singular Markovian jump systems, whereas the existing research studies in literature focused on state‐feedback or static output‐feedback control. While they have only provided the sufficient conditions, this paper successfully obtains the necessary and sufficient condition for the existence of the dynamic output‐feedback control. Furthermore, this condition is expressed with linear matrix inequalities by the so‐called replacement technique. Two numerical examples show the validity of the resulting control. 相似文献
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This paper deals with the class of linear discrete-time systems with random abrupt changes also known as class of Markovian jump singular systems. The problems of stochastic stability and the stochastic stabilisation (using state-feedback control and static output feedback control) are tackled. Conditions in the LMI setting to design the appropriate gains of the controllers are developed. It is shown that all the addressed problems can be solved if the corresponding developed linear matrix inequalities (LMIs) are feasible. Numerical examples are employed to show the usefulness of the proposed results. 相似文献
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In this paper, the static output feedback decentralized stabilization problem is addressed using a linear matrix inequality approach. A necessary and sufficient condition for static output feedback decentralized stabilizability is derived for linear time-invariant large-scale systems. It is proven that the existence of a stabilizing decentralized gain is equivalent to that of the solution of a quadratic matrix inequality. The extension of the result to
control is studied. An iterative LMI algorithm based on the linear matrix inequality technique is proposed to obtain the decentralized feedback gain. Examples show the effectiveness of the algorithm. 相似文献
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The problem of robust stabilisation for uncertain discrete singular systems with time-varying delay is discussed in this article. First, a new delay-distribution-dependent Lyapunov function is established. Then, sufficient conditions are proposed for guaranteeing that the uncertain discrete singular system with time-varying delay has the properties of regularity, causality and stability. Finally, a suitable robust state feedback controller is designed by linear matrix inequality. Numerical examples illustrate that the results derived from the proposed method are less conservative than the existing ones. 相似文献
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This paper investigates the problem of delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays in terms of linear matrix inequality (LMI) approach. Based on a delay-dependent stability condition for the nominal system, a state feedback controller is designed, which guarantees the resultant closed- loop system to be robustly stable. An explicit expression for the desired controller is also given by solving a set of matrix inequalities. Some numerical examples are provided to illustrate the less conservativeness of the proposed methods. 相似文献
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This paper investigates the problem of delay-dependent robust stabilization for uncertain singular systems with discrete and distributed delays in terms of linear matrix inequality (LMI) approach. Based on a delay-dependent stability condition for the nominal system, a state feedback controller is designed, which guarantees the resultant closedloop system to be robustly stable. An explicit expression for the desired controller is also given by solving a set of matrix inequalities. Some numerical examples are provided to illustrate the less conservativeness of the proposed methods. 相似文献
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The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which are normal linear time-delay systems, and the corresponding design steps are presented via linear matrix inequality(LMI). Moreover, the observer-based feedback stabilizing controller is obtained. Three examples are given to show the effectiveness of the proposed methods. 相似文献
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Observer design and output feedback stabilization for linear singular time-delay systems with unknown inputs 总被引:1,自引:1,他引:0
The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which are normal linear time-delay systems, and the corresponding design steps are presented via linear matrix inequality(LMI). Moreover, the observer-based feedback stabilizing controller is obtained. Three examples are given to show the effectiveness of the proposed methods. 相似文献
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Admissibility and static output‐feedback stabilization of singular Markovian jump systems with defective statistics of modes transitions
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This paper presents a necessary and sufficient condition for discrete‐time singular Markovian jump linear systems with defective statistics of modes transitions to be regular, causal, and stochastically stable. The static output‐feedback stabilization problem for discrete‐time singular Markovian jump linear system with defective statistics of modes transitions is studied. Furthermore, the defective statistics about modes transitions are studied by considering the uncertain transition probabilities and partially unknown transition probabilities situations account in a composite way. The closed‐loop system is represented in an augmented form, in which input and gain‐output matrices are separated. By virtue of the system augmentation, a sufficient condition for the existence of desired controllers is established. An extension to mode‐independent static output‐feed stabilization is provided as well. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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The robust stability and robust stabilization for time‐delay discrete singular systems with parameter uncertainties is discussed. A delay‐dependent linear matrix inequality (LMI) condition for the time‐delay discrete systems to be nonsingular and stable is given. Based on this condition and the restricted system equivalent transformation, the delay‐dependent LMI condition is proposed for the time‐delay discrete singular systems to be admissible. With this condition, the problems of robust stability and robust stabilization are solved, and the delay‐dependent LMI conditions are obtained. Numerical examples illustrate the effectiveness of the method given in the paper. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society 相似文献