【作者】 孙琦；

【导师】 孙希明；

【作者基本信息】 大连理工大学 ， 控制理论与控制工程， 2015， 硕士

【摘要】 切换时滞系统模型是一类同时受到切换行为与时滞现象影响的数学模型,在实际工程问题中有着广泛的应用背景,对其进行性能分析与控制设计一直是控制领域的研究热点。特别是稳定性问题,更是研究的焦点所在。由于切换动作与时滞现象都含有不稳定因素,都可能会引起系统状态的不稳定,而在切换时滞系统中,二者相互作用,使得这种系统的稳定性问题变得愈加复杂,许多相关问题亟待解决。由于切换与时滞的共同存在,实际控制系统常常带有不稳定模态,甚至出现系统模态都不稳定的情况,例如网络化控制系统、多智能体系统等。子系统都不稳定的切换时滞系统在实际工程中普遍存在,对其进行稳定性分析具有重要的理论意义与实际价值。本文首次使用驻留时间方法对子系统都不稳定的切换时滞系统进行稳定性理论分析。首先使用多Lyapunov泛函方法,在驻留时间限制下,给出了子系统都不稳定的非线性切换时滞系统的指数稳定性条件。在此基础上,将结果应用在子系统都不稳定的线性切换时滞系统中,使用线性插值方法,得到了离散化Lyapunov泛函,并在此基础上以线性矩阵不等式的形式建立了相应系统的指数稳定性判定条件。最后,通过数值实例仿真,验证了所给结果的有效性。更多还原

【Abstract】 Switched delay systems are a class of models which are affected simultaneously by switching behavior and delay phenomenon. This class of systems plays an important role in control theory and control engineering and much attention has been paid to performance analysis and controller design for such systems, where one of the basic problems is the stability analysis for it. As we all known, both switching behavior and delays can make a system unstable. Therefore, the analysis for switching delay systems is more complicated under the interaction of switching behavior and delays. Many problems related to such a system remain unsolved.Affected by switching behavior and delays, the switched delay systems may contain unstable subsystems. In the extreme situation, all subsystems may become unstable, such as, the networked control systems, multi-agent systems, etc. Since switched delay systems with all unstable subsystems are often encountered in engineering and practical applications, stability analysis of such systems is of great significance both in theory development and practical applications.In this paper, stability analysis is presented for the switched delay systems with all subsystems unstable for the first time by dwell time approaches. Firstly, by adopting the techniques of multiple Lyapunov functional, the exponentially stable conditions are developed for the nonlinear switched delay systems with all unstable subsystems under the constraint of dwell time. Then, the obtained results are applied to linear switched delay systems with all unstable subsystems. Then by utilizing the linear interpolation technique, a novel discrete Lyapunov functional is constructed, based on which the exponentially stable conditions for such a linear system is proposed in the form of linear matrix inequalities (LMIs). Finally, a numerical example is given to show the effectiveness of the proposed results.更多还原