时变时滞系统时滞依赖稳定性分析及状态反馈控制
发布时间：2019-05-24 04:46
【摘要】：在控制理论的研究中,时滞系统备受关注。时滞存在于自然界的各种系统之中,它严重影响系统的动态性能。如果需要构建更加精确的模型,就不能忽略时滞对系统性能的影响,所以研究时滞系统具有重要的理论价值和实际意义。但是,目前很难找到一种普遍适用的方法解决此类问题,所以需要采用不同的方法研究各类时滞系统。本文基于前人的工作,对线性区间时变时滞系统和非线性Luire时变时滞系统进行深入研究。构造包含更多信息的Lyapunov泛函,采用减少放大程度的界定方法都可以有效优化结果。考虑线性区间时变时滞系统,在构造Lyapunov泛函时,尽可能包含更多的时滞信息,并通过Jensen不等式结合倒数凸组合方法和Jensen不等式结合自由权矩阵方法界定泛函导数积分项,得到时滞依赖稳定性判据。考虑非线性Lurie时变时滞系统,在构造Lyapunov泛函时,尽可能包含更多的系统信息,通过Wirtinger不等式结合倒数凸组合方法界定泛函导数积分项,并应用S-procedure过程处理泛函导数,得到时滞依赖稳定性判据。通过MATLAB仿真求解线性矩阵不等式,从而得到使系统渐近稳定的Lyapunov泛函。基于系统的稳定性判据,给出系统满足H_∞性能的充分条件,并设计系统的状态反馈控制器。通过MATLAB仿真求得系统的反馈增益矩阵并搭建Simulink模型。最后通过数值算例验证结果的正确性。
[Abstract]:In the study of control theory, time-delay systems have attracted much attention. Time delay exists in various systems in nature, which seriously affects the dynamic performance of the system. If a more accurate model is needed, the influence of time delay on system performance can not be ignored, so it is of great theoretical and practical significance to study time-delay systems. However, it is difficult to find a universal and applicable method to solve this kind of problem, so it is necessary to use different methods to study all kinds of time-delay systems. In this paper, based on the previous work, linear interval time-varying time-delay systems and nonlinear Luire time-varying time-delay systems are deeply studied. The Lyapunov functional with more information can be constructed, and the results can be effectively optimized by using the definition method to reduce the magnification. In this paper, linear interval time-varying time-delay systems are considered. When constructing Lyapunov Functionals, more delay information is included as much as possible, and the functional derivative integral terms are defined by Jensen inequality combined with reciprocal convex combination method and Jensen inequality combined with free matrix method. The delay dependent stability criterion is obtained. In this paper, nonlinear Lurie time-varying time-delay systems are considered. When constructing Lyapunov Functionals, more system information is included as much as possible. The functional derivative integral term is defined by Wirtinger inequality combined with reciprocal convex combination method, and the functional derivatives are dealt with by S-procedure process. The delay dependent stability criterion is obtained. The linear matrix inequality (LMI) is solved by MATLAB simulation, and the Lyapunov functional which makes the system asymptotically stable is obtained. Based on the stability criterion of the system, the sufficient conditions for the system to satisfy the H _ 鈭，
本文编号：2484570
[Abstract]:In the study of control theory, time-delay systems have attracted much attention. Time delay exists in various systems in nature, which seriously affects the dynamic performance of the system. If a more accurate model is needed, the influence of time delay on system performance can not be ignored, so it is of great theoretical and practical significance to study time-delay systems. However, it is difficult to find a universal and applicable method to solve this kind of problem, so it is necessary to use different methods to study all kinds of time-delay systems. In this paper, based on the previous work, linear interval time-varying time-delay systems and nonlinear Luire time-varying time-delay systems are deeply studied. The Lyapunov functional with more information can be constructed, and the results can be effectively optimized by using the definition method to reduce the magnification. In this paper, linear interval time-varying time-delay systems are considered. When constructing Lyapunov Functionals, more delay information is included as much as possible, and the functional derivative integral terms are defined by Jensen inequality combined with reciprocal convex combination method and Jensen inequality combined with free matrix method. The delay dependent stability criterion is obtained. In this paper, nonlinear Lurie time-varying time-delay systems are considered. When constructing Lyapunov Functionals, more system information is included as much as possible. The functional derivative integral term is defined by Wirtinger inequality combined with reciprocal convex combination method, and the functional derivatives are dealt with by S-procedure process. The delay dependent stability criterion is obtained. The linear matrix inequality (LMI) is solved by MATLAB simulation, and the Lyapunov functional which makes the system asymptotically stable is obtained. Based on the stability criterion of the system, the sufficient conditions for the system to satisfy the H _ 鈭，
本文编号：2484570
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