共查询到19条相似文献,搜索用时 62 毫秒
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研究了正线性系统的共同线性copositive Lyapunov函数。首先,基于几何性质给出了关于一对二阶正线性系统的定理的另一种证明。通过新的证明方法,把结果推广到有限个二阶正线性系统的情况.然后对三阶情况给出了一个结果。最后,对高阶的正线性系统给出了一些结果。 相似文献
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研究了寻找三阶系统族的共同二次Lyapunov函数问题.针对给定的稳定的三阶系统提出了寻找二次Lyapunov函数集的方法,然后获得了三阶系统族具有共同二次Lyapunov函数的充分条件.该充分条件易于构造,从而具有较强的工程实用性.文中实例验证了所得结果的有效性. 相似文献
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一类线性切换系统的鲁棒状态反馈镇定 总被引:1,自引:0,他引:1
考虑一类标称系统存在共同Lyapunov函数的切换系统的鲁棒镇定问题.在不确定性不满足匹配条件下,设计出鲁棒状态反馈控制器,并在给定的切换策略下,确保闭环系统在其平衡点处渐近稳定.仿真结果表明所设计控制器是有效的. 相似文献
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利用时滞分解和平均驻留时间方法讨论一类时滞切换系统的稳定性问题.定义了更为一般的Lyapunov函数,结合Jensen积分不等式和倒数凸组合技术得到的线性矩阵不等式条件具有更小的保守性和更低的计算复杂性给出的仿真算例进一步验证了所得结果的有效性. 相似文献
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切换系统作为一类典型的混杂系统,近年来在国内外受到极大重视。实际工程中,由于切换过于频繁难以使系统保持稳定,针对切换时间间隔受限的情况,研究一类离散线性切换系统的稳定性。利用李亚普诺夫稳定性理论,给出系统满足稳定性的充分条件,并利用此条件设计出相应的切换控制规律和状态反馈子控制器。最后对包含两个离散子系统的切换系统进行了仿真计算,其结果验证了文中所给出定理的有效性。 相似文献
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It is undoubtedly important to be able to ensure the existence of a common quadratic Lyapunov function (CQLF) for a given switched system because this is proof of its asymptotic stability, but equally important is the ability to calculate it in order to obtain more specific information about the behaviour of the switched system under analysis. This article describes the development of a new methodology for calculating a CQLF based on particle swarm optimisation (PSO) once the existence of a CQLF has been assured. Several comparative analyses are presented to show the strengths and advantages of the proposed methodology. 相似文献
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This article is concerned with the existence problem of a common linear copositive Lyapunov function (CLCLF) for switched positive linear systems with stable and pairwise commutable subsystems. Three families of such systems composed of only continuous-time subsystems, only discrete-time subsystems and mixed continuous- and discrete-time subsystems are considered, respectively. It is demonstrated that a CLCLF can always be constructed for the underlying system whenever its subsystems are continuous-time, discrete-time or the mixed type. The case when the number of subsystems is two is first considered, then the obtained result is extended to the general case. Three numerical examples are given to verify the validity of the developed results. 相似文献
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Finite‐time stability of switched nonlinear time‐varying systems via indefinite Lyapunov functions 下载免费PDF全文
This note considers the problem of finite‐time stability (FTS) for switched nonlinear time‐varying systems. First, a relaxed condition is proposed to verify the FTS of nonlinear time‐varying systems by using an indefinite Lyapunov function. Then, the result obtained is extended to study the FTS of switched nonlinear time‐varying systems. Several relaxed conditions are given by using a common indefinite Lyapunov function and multiple indefinite Lyapunov functions. Moreover, the corresponding estimates on convergence regions and times of systems are also given. Comparing with the existing results, the conditions obtained allow the time derivative of Lyapunov functions of subsystems (or systems) to be indefinite and all subsystems to be not finite‐time stable or even unstable. Finally, a numerical example is given to illustrate the theoretical results. 相似文献
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This paper investigates the problem of global disturbance rejection for switched nonlinear systems in strict‐feedback form with unknown exosystem where the solvability of the disturbance rejection problem for subsystems is not assumed. First, a sufficient condition for the solvability of the global disturbance rejection problem is given. As an extension of the classic concept of internal model for non‐switched systems, a new concept of switched internal model is proposed. Second, in order to solve the problem in question, a constructive adaptive control methodology is established on the basis of the multiple Lyapunov functions method, backstepping, and the changing supply functions technique. Finally, an example is provided to demonstrate the effectiveness of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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Stabilizability of switched linear systems does not imply the existence of convex Lyapunov functions
Counterexamples are given which show that a linear switched system (with controlled switching) that can be stabilized by means of a suitable switching law does not necessarily admit a convex Lyapunov function. Both continuous- and discrete-time cases are considered. This fact contributes in focusing the difficulties encountered so far in the theory of stabilization of switched system. In particular the result is in contrast with the case of uncontrolled switching in which it is known that if a system is stable under arbitrary switching then admits a polyhedral norm as a Lyapunov function. 相似文献
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This paper investigates the problem of global adaptive finite-time stabilisation for a class of switched nonlinearly parameterised systems. Without requiring that each subsystem is globally adaptively finite-time stabilisable, a switched adaptive finite-time control scheme is developed by exploiting the multiple Lyapunov functions method and adding a power integrator technique. By using the parameter separation technique, the unknown parameters are separated from nonlinear functions. On the basis of finite-time Lyapunov stability theory, it is proved that the proposed controller can guarantee that the state of the resulting closed-loop system converges to the origin in finite time. Finally, an example is given to demonstrate the effectiveness of the proposed method. 相似文献
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This paper addresses the stability issue of discrete-time switched systems with guaranteed dwell-time. The approach of switched homogeneous Lyapunov function of higher order is formally proposed. By means of this approach, a necessary and sufficient condition is established to check the exponential stability of the considered system. With the observation that switching signal is actually arbitrary if the dwell time is one sample time, a necessary and sufficient condition is also presented to verify the exponential stability of switched systems under arbitrary switching signals. Using the augmented argument, a necessary and sufficient exponential stability criterion is given for discrete-time switched systems with delays. A numerical example is provided to show the advantages of the theoretical results. 相似文献