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研究了一类具有凸多面体不确定性的离散时滞广义系统的鲁棒稳定性问题。基于参数依赖的Lyapunov函数和线性矩阵不等式方法,推导出使系统正则、因果且鲁棒稳定的时滞相关型充分条件。算例验证了本文方法的可行性。 相似文献
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离散广义系统的鲁棒稳定性 总被引:1,自引:1,他引:0
针对具有结构不确定性的离散广义系统,提出了一种新的鲁棒稳定性分析方法;得到了使所考虑系统鲁棒稳定的条件,该条件保证对所有容许的结构摄动,离散广义系统正则、因果且稳定;并进一步得到了所考虑系统具有鲁棒极点集的条件. 相似文献
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离散广义区间动力系统的稳定性 总被引:1,自引:0,他引:1
利用范数理论,研究离散广义区间动力系统的稳定性问题,给出其区间动力系统的正则、因果且稳定的充分条件.在此基础上,进一步考虑该系统的区间极点集的配置问题,给出了使离散广义区间动力系统的极点落在预先给定园盘内的判定定理.数值算例表明了该方法的可行性. 相似文献
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利用Lyapunov函数方法、系统分解法以及矩阵不等式等方法研究一类具有脉冲行为的广义互联大系统的渐近稳定性及分散镇定问题,在子系统正则且零解渐近稳定的条件下,给出广义线性互联大系统的渐近稳定莉定的一个充分条件,并设计适当的反馈律,以实现广义互联大系统的镇定。通过仿真实例说明主要结果。 相似文献
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广义系统具有正定解的Lyapunov方程 总被引:1,自引:0,他引:1
本文研究线性广义系统有正定解的Lyapunov方程,给出广义系统稳定等价于Lyapunov方程有正定解,进一步研究了广义系统R-能观,稳定和Lyapunov方程存在正定解三者之间的关系。基于该Lyapunov方程,给出广义系统允许(正则,稳定,无脉冲)的等价条件。 相似文献
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引入2-D奇异一般离散状态空间模型的Lyapunov方程,探讨了该模型的渐近稳定性、特征多项式的根式以及2-D Lyapunov矩阵方程间的关系,给出了系统渐近稳定性的充分条件。 相似文献
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Hybrid singular systems of differential equations 总被引:4,自引:0,他引:4
This work develops hybrid models for large-scale singular differential system and analyzes their asymptotic properties. To take into consideration the discrete shifts in regime across which the behavior of the corresponding dynamic systems is markedly different, our goals are to develop hybrid systems in which continuous dynamics are intertwined with discrete events under random-jump disturbances and to reduce complexity of large-scale singular systems via singularly perturbed Markov chains. To reduce the complexity of large-scale hybrid singular systems, two-time scale is used in the formulation. Under general assumptions, limit behavior of the underlying system is examined. Using weak convergence methods, it is shown that the systems can be approximated by limit systems in which the coefficients are averaged out with respect to the quasi-stationary distributions. Since the limit systems have fewer states, the complexity is much reduced. 相似文献
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Asymptotic stability in probability and stabilization for a class of discrete‐time stochastic systems
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J. Yin 《国际强度与非线性控制杂志
》2015,25(15):2803-2815
》2015,25(15):2803-2815
This paper investigates asymptotic stability in probability and stabilization designs of discrete‐time stochastic systems with state‐dependent noise perturbations. Our work begins with a lemma on a special discrete‐time stochastic system for which almost all of its sample paths starting from a nonzero initial value will never reach the origin subsequently. This motivates us to deal with the asymptotic stability in probability of discrete‐time stochastic systems. A stochastic Lyapunov theorem on asymptotic stability in probability is proved by means of the convergence theorem of supermartingale. An example is given to show the difference between asymptotic stability in probability and almost surely asymptotic stability. Based on the stochastic Lyapunov theorem, the problem of asymptotic stabilization for discrete‐time stochastic control systems is considered. Some sufficient conditions are proposed and applied for constructing asymptotically stable feedback controllers. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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The purpose of this paper is to develop new methods for constructing vector Lyapunov functions and broaden the application of Lyapunov's theory to stability analysis of large-scale dynamic systems. The application, so far limited by the assumption that the large-scale systems are composed of exponentially stable subsystems, is extended via the general concept of comparison functions to systems which can be decomposed into asymptotically stable subsystems. Asymptotic stability of the composite system is tested by a simple algebraic criterion. By redefining interconnection functions among the subsystems according to interconnection matrices, the same mathematical machinery can be used to determine connective asymptotic stability of large-scale systems under arbitrary structural perturbations. With minor technical adjustments, the theory is broadened to include considerations of unstable subsystems as well as instability of composite systems. 相似文献
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This paper addresses the problem of stability analysis for homogeneous large-scale uncertain bilinear time-delay systems subjected to constrained inputs. Both nonlinear uncertainties and interval systems are discussed. Several delay-independent criteria are presented to guarantee the asymptotic stability of the overall systems. The main feature of the presented criteria is that although the Lyapunov stability theorem is used, they do not involve any Lyapunov equations that may be unsolvable. Three illustrative numerical examples are presented to verify the effectiveness of the proposed stability criteria. 相似文献