Article

Stability, robust stabilization and H∞ control of singular-impulsive systems via switching control

Department of Control Science and Engineering, Huazhong University of Science and Technology, Wu-han-shih, Hubei, China
Systems & Control Letters (Impact Factor: 1.89). 11/2006; 55(11):879-886. DOI: 10.1016/j.sysconle.2006.05.002
Source: DBLP

ABSTRACT In this paper, stability, robust stabilization and H∞ control of singular-impulsive systems are studied. Some new fundamental properties are derived for switched singular systems subject to impulse effects. Applying the Lyapunov function theory, several sufficient conditions are established for exponential stability, robust stabilization and H∞ control of the corresponding singular-impulsive closed-loop systems. Some numerical examples are given to demonstrate the effectiveness of the proposed control and stabilization methods.

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    • "在切换系统 的实际工作过程中, 由于受到外在环境的干扰或内在 系统发生故障等原因, 系统的切换往往伴随着脉冲行 为, 即系统的运行轨迹发生一定的跳变, 这类系统被 称为脉冲切换系统. 目前, 对脉冲切换系统的研究大 都集中在稳定性方面 [9] [10] [11] [12] [13] [14] "
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    ABSTRACT: Optimal control problems are investigated for a class of impulsive and switching systems, where the transitions are state-dependent. Two kinds of situations for the cost function are considered. When the cost function is smooth, by parameterizing the jumping instants as a new parameter to be optimized, the necessary optimality conditions of the hybrid systems are obtained. When the cost functional is nonsmooth, necessary optimality conditions of the generalized differential form are presented by the knowledge of nonsmooth analysis. An example is given to illustrate the effectiveness of the proposed method.
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    • "They are encountered in chemical processes, mineral industries, electronic and economics systems [3], [4], [5]. In recent years a great deal of works has been devoted to the analysis and design techniques for singular systems [6], [7], [9], [8], [10]. On the other hand, switched systems have received a lot of attention during the last decade. "
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    ABSTRACT: This paper concerns the stability and the stabilization of discrete-time singular switched systems. Sufficient conditions for a discrete-time singular switched system to be admissible are expressed in strict Linear Matrix Inequalities (LMIs) terms. Design of state feedback controllers are then proposed in strict LMIs. For more relaxation, slack variables are introduced. These results are extended to static output feedback controller design. Numerical example is given to illustrate the proposed methods.
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    • "Other efforts [4] [5] [6] [7] have addressed the stabilization problem of CDNs by utilizing different control strategies, such as the pinning control strategy [4] [5], the decentralized control strategy [6], the hybrid control strategy [7], and so on. On the other hand, singular systems have attracted particular attention in the scientific community largely due to the important applications in different fields, such as circuits, biological and mechanical systems and so on [8]. In particular, singular systems can still model physical systems in some cases when state-space ones are not applicable [13] [14]. "
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    ABSTRACT: This paper presents a general uncertain complex singular dynamical network model. Since the nodes of the network are singular systems, the overall network can only be described by a singular model. Due to the flexible of singular systems in describing practical applications, the complex singular dynamical network has more applications than the regular complex network in which the nodes are described by the state-space dynamical systems. Robust stabilization of such uncertain complex singular dynamical network is investigated via impulsive control. Based on the Lyapunov stability theory, sufficient conditions for the stabilization of the uncertain complex singular dynamical network are obtained under impulsive control. A systematic-design procedure is presented, and a numerical example is provided for illustration.
    Proceedings of the 48th IEEE Conference on Decision and Control, CDC 2009, combined withe the 28th Chinese Control Conference, December 16-18, 2009, Shanghai, China; 01/2009
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