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: 2.06). 11/2006; 55(11):879-886. DOI: 10.1016/j.sysconle.2006.05.002
Source: DBLP


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.
    Kongzhi yu Juece/Control and Decision 02/2014; 29(1). DOI:10.13195/j.kzyjc.2012.1475
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    • "So it is very important to discuss the problem of impulsive control. For the stability of the impulsive control system, nonlinear impulsive control was put forward and the concept of asymptotic stability condition was provided in [11]. Asymptotic stability condition for a class of uncertain impulsive system was established through the comparison theorem in [12]. "
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    ABSTRACT: Globally exponential stability of Complex (with coupling) Nonlinear Singular Impulsive Networked Control Systems (CNSINCS) with packet dropouts and time-delay is investigated. Firstly, the mathematic model of CNSINCS is established. Then, by employing the method of Lyapunov functional, exponential stability criteria are obtained and the impulsive controller design method is given. Finally, some simulation results are provided to demonstrate the effectiveness of the proposed method.
    Mathematical Problems in Engineering 01/2013; 2013:1-6. DOI:10.1155/2013/741908 · 0.76 Impact Factor
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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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