【作者】 张榆平；

【导师】 朱宏；

【作者基本信息】 电子科技大学 ， 测试计量技术与仪器， 2007， 博士

【摘要】 切换中立型时滞系统是一类重要的混杂系统。由于这类系统中既有连续动态,又有离散动态,还有中立型时滞的交互作用,所以许多工程实际问题可以用这样的系统模型来描述,具有广泛的工程实际背景和理论研究意义。本文以Lyapunov稳定性理论为基础,采用线性矩阵不等式方法,研究了切换中立型时滞系统的稳定性分析与设计的一些问题,涉及的主要工作如下:第一,根据时滞大小和切换间隔的关系,研究切换中立型时滞系统在任意切换序列情况下的渐近稳定性问题。通过对系统进行等效变换,利用Lyapunov泛函方法,研究各个子系统的结构对整个切换系统稳定性的影响,然后以线性矩阵不等式的形式给出使系统渐近稳定的充分条件,同时给出系统带记忆的状态反馈控制器的设计方法。第二,研究了一类固定切换律的切换中立型系统的指数稳定性问题。根据现实世界里许多切换控制系统的切换信号是状态依赖型的情形,对一类切换域固定的切换中立型系统,通过Lyapunov泛函方法和不等式分析技巧研究了其等效变换系统的E-指数稳定性,然后根据两系统稳定性之间的等效性,得到原系统指数稳定的充分条件,在此基础上给出时滞状态反馈控制器的设计方法。第三,研究了一类切换中立型系统的切换律设计问题。对于系数矩阵存在Hurwitz线性凸组合的一组中立型时滞子系统,可以通过状态空间的合理划分,找到子系统渐近稳定的区域,据此构造切换域并得到切换律的设计方案,并以线性矩阵不等式的形式给出自治切换系统渐近稳定的充分条件。这里研究的子系统不一定是稳定的,只需要满足一定的约束,而切换律起到了稳定系统的关键作用。对于不满足约束的情况,可以通过设计切换状态反馈控制器和相应的切换律,使闭环系统渐近稳定。第四,研究了一类不确定切换中立型系统的鲁棒非脆弱H_∞控制问题。通过研究确定切换中立型系统的H_∞性能问题,给出系统内稳定的条件以及无记忆状态反馈控制器的设计方法。在此结论的基础上,将其推广到系统结构中存在有界不确定的情形,并兼顾考虑控制器增益扰动的影响,设计出带有H_∞性能的鲁棒非脆弱控制器。第五,研究了切换中立型系统的保成本可靠控制问题。利用连续故障模型,针对实际控制系统中执行器非理想化的事实,构造出更接近实际的系统模型,利用Lyapunov泛函法,考虑二次成本函数的约束,给出了系统保成本可靠控制器的设计方法,并通过优化方法得到成本函数的上界值。最后,研究了切换中立型系统的鲁棒滑模控制问题。对存在线性分式不确定性的切换中立型系统,利用Lyapunov方法,结合Finsler引理对每个子系统分别设计滑模面和控制器,使系统在任意切换律作用下均能满足到达条件和滑模运动稳定条件。在此基础上研究了设计单一滑模面和切换律来共同稳定系统的方法。论文的结束部分对全文所做的工作进行了总结,并指出了下一步研究的方向。更多还原

【Abstract】 A switched neutral delay system is an important category of hybrid systems. Due to interaction among the continuous dynamics and discrete dynamics and neutral time-delay is common in this kind of systems, many practical engineering issues can be described by switched neutral delay systems, the research of switched neutral delay systems is significant for both practice and theory. Based on Lyapunov stability theory, this dissertation mainly investigates the stability analysis and design of switched neutral delay systems by linear matrix inequalities method. The main contributions of this dissertation are as follows.Firstly, based on the relationship between time-delay and switching interval, the asymptotic stability of switched neutral delay systems under arbitrary switching sequence is discussed. The equivalent transformation is done to research the effect of configuration of subsystems to the stability of the whole system by Lyapunov functional method. Then sufficient conditions are given to guarantee asymptotic stability of switched neutral delay systems in term of linear matrix inequalities. Also, the design of state feedback controllers with memory is established.Secondly, exponential stability of switched neutral delay systems with fixed switching law is addressed. Since it is ture that state-dependent switching signals are usual in many switched control systems in real world, E-exponential stability of equivalent systems with fixed switching region is investigated by Lyapunov functional methods and inequalities analysis technique. Owning to the stability equivalence between the two systems, exponential stability of original system is obtained. Corresponding design of state feedback controllers are also accomplished on this basis.Thirdly, switching law design of a class of switched neutral delay systems is studied. If there is a Hurwitz linear convex combination of coefficient matrices for a class of neutral delay subsystems, asymptoticly stable regions of each subsystem can be found by dividing the state space properly. Based on the divisions of state space, switching law can be obtained by setting switching regions. Sufficient conditions of this kind of switched neutral systems are provided in term of linear matrix inequalities. Here, the stability of subsystems is not necessary, they are only required to satisfy certain conditions. Switching laws are crucial to stabilize the whole system in these problems. Switching state feedback controllers and switching laws can also be designed to make the close-loop system stable for those which do not meet the constraint conditions.Fouthly, the problem of robust non-fragile H_∞control is discussed for a class of uncertain switched neutral delay systems. H_∞performance of definite switched neutral delay systems is discussed in advance, and the condition of interior stability and design of corresponding state feedback controllers without memory are presented. These results are extended to uncertain switched neutral delay systems, influence of gain disturbance of controllers is also considered. And then, controllers of robust non-fragile with H_∞performance are obtained.Next, reliable guaranteed cost control problem of switched neutral delay systems is concerned. Based on the fact that actuators are nonideal in real control systems, a more practical system is constructed by using continuous faults model. Reliable guaranteed cost controllers with constraint of quadratic cost function are obtained by the method of Lyapunov functional. Upper bound of the cost function can be derived by optimal methods.Finally, the problem of robust sliding control of switched neutral delay systems is studied. Combined the Lyapunov method with Finsler’s lemma, sliding surfaces and corresponding controllers of each subsystems are designed, which meet reching conditions and sliding mode conditions for switched neutral delay systems with linear fractional uncertainty under arbitrary switching laws. Based on these results, the design of single sliding surface and switching laws are also presented to make systems stable.At the end of the dissertation, the results are summarized and further research problems are pointed out.更多还原