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1.
基于LMIs处理方法,研究了一类不确定线性切换系统在任意切换下的鲁棒控制问题.利用矩阵Schur补引理构造线性矩阵不等式,得到该系统的鲁棒稳定性的充要条件,同时也给出了在状态反馈下的鲁棒稳定性充要条件和在输出反馈下的充分条件.最后用数值例子对所得结果加以验证,说明了文中结果的正确性.  相似文献   

2.
主要研究了镇定切换系统的鲁棒稳定性问题.用切换lyapunov函数方法,通过定义指标函数,讨论了基于切换lyapunov函数的若干类时滞切换系统的稳定性问题,用矩阵不等式研究了时滞,时滞摄动和不确定时滞的切换系统的鲁棒稳定性.  相似文献   

3.
邱亚林 《数学研究》2000,33(4):432-438
考虑一类具有时滞的线性时变区间系统的鲁棒稳定及鲁棒稳定化问题。利用矩阵测度及时滞积分不等式,得到了它们的判定条件。此外,在相同条件下,讨论了该类系统的BIBO稳定性,最后举二例说明本结果的有效性。  相似文献   

4.
非线性离散开关系统的鲁棒镇定问题   总被引:1,自引:0,他引:1  
利用切换Lypunov函数方法,把非线性离散开关系统的鲁棒镇定问题转化成一个矩阵不等式的最优解问题,给出了在任意切换下具有非线性扰动的线性开关系统的可鲁棒镇定的充分条件,并进一步讨论了同类时滞开关系统的鲁棒镇定问提.最后把以上结论推广到广义开关系统,由于结果均以矩阵不等式形式给出,便于验证和实现.  相似文献   

5.
李伯忍 《应用数学》2016,29(4):788-796
本文研究一类具有参数不确定性的线性中立型时变时滞系统的鲁棒稳定性.首先,利用Jensen’s不等式,并采用新方法来处理积分项,得到标称中立型系统的稳定性判据.然后,基于标称系统的稳定性结果,进一步得到系统矩阵存在不确定性时的鲁棒稳定性判据.本文的新方法能充分利用负定项的信息,故稳定性结果的保守性更低.最后,两个数值例子分别验证了文中所得的标称中立型系统稳定性判据的保守性更低,以及系统矩阵存在不确定性时的鲁棒稳定性判据的可行性.  相似文献   

6.
通过使用灰色矩阵覆盖集的分解方法和矩阵范数的性质,构造李雅普诺夫函数,研究了灰色中立随机线性时滞系统的鲁棒稳定性和几乎指数鲁棒稳定性.  相似文献   

7.
研究了具有时间滞后切换不确定细胞神经网络(UCNNs)系统的指数稳定性.利用同胚映射和M矩阵理论,得到UCNNs系统平衡点存在性,唯一性和指数稳定性的充分条件;利用平均驻留时间方法,研究了时滞切换UCNNs系统限制切换下的鲁棒指数稳定性,并得到确保系统全局指数稳定的充分条件.  相似文献   

8.
针对具有任意切换序列的不确定线性切换系统,提出一种鲁棒镇定切换控制律设计方法.通过求解一组线性矩阵不等式,计算切换系统的共同鲁棒控制Lyapunov函数,进而构造一个双自由度的切换状态反馈控制律.应用共同鲁棒控制Lyapunov函数性质和切换控制理论,证明所提切换控制律的鲁棒渐近稳定性和逆最优性及共同鲁棒扇形裕度(0.5,∞).最后以DC-DC升压变换器切换控制为例,仿真验证文章方法的有效性和实用性.  相似文献   

9.
在基于Lyapunov-Krasovskii泛函、Schur补引理及矩阵不等式方法下,讨论了一类具有变时滞不确定性Lurie切换系统,在切换状态输出反馈策略下,得到了鲁棒H_∞控制性能要求下可行解存在的充分性判据,为系统的综合提供了可行性判据.设计了有记忆的输出反馈控制器以及切换规则,且有记忆控制器的设计,为系统的稳定性分析及控制器的综合提供了更多的自由度,最后的结果转化为线性矩阵不等式给出,通过数值仿真,验证了定理的有效性和实用性.  相似文献   

10.
薛焕斌 《应用数学》2018,31(1):108-116
本文研究具有时间滞后和脉冲效应的切换区间细胞神经网络的鲁棒指数稳定性.利用M-矩阵的性质和平均驻留时间方法,研究了时滞切换脉冲神经网络在参数扰动和限制切换下的指数稳定性,并得到确保系统全局指数稳定的充分条件.得到的结论是显式结构,有利于实际工程应用.  相似文献   

11.
In this note, a common quadratic Lyapunov function is explicitly calculated for a linear hybrid system described by a family of simultaneously triangularizable matrices. The explicit construction of such a function allows not only obtaining an estimate of the convergence rate of the exponential stability of the switched system under arbitrary switching but also calculating an upper bound for the output during its transient response. Furthermore, the presented result is then extended to the case where the system is affected by parametric uncertainty, providing the corresponding results in terms of the nominal matrices and uncertainty bounds.  相似文献   

12.
This paper is concerned with the robust stabilization problem for a class of linear uncertain stochastic systems with Markovian switching. The uncertain stochastic system with Markovian switching under consideration involves parameter uncertainties both in the system matrices and in the mode transition rates matrix. New criteria for testing the robust stability of such systems are established in terms of bi-linear matrix inequalities (BLMIs), and sufficient conditions are proposed for the design of robust state-feedback controllers. A numerical example is given to illustrate the effectiveness of our results.  相似文献   

13.
In this work, robust stability in distribution of Boolean networks (BNs) is studied under multi-bits probabilistic and markovian function perturbations. Firstly, definition of multi-bits stochastic function perturbations is given and an identification matrix is introduced to present each case. Then, by viewing each case as a switching subsystem, BNs under multi-bits stochastic function perturbations can be equivalently converted into stochastic switching systems. After constructing respective transition probability matrices which can unify multi-bits probabilistic and markovian function perturbations in a consolidated framework, robust stability in distribution can be handled. On such basis, necessary and sufficient conditions for robust stability in distribution of BNs under stochastic function perturbations are given respectively. Finally, two numerical examples are presented to verify the validity of our theoretical results.  相似文献   

14.
A problem of robust guaranteed cost control of stochastic discrete-time systems with parametric uncertainties under Markovian switching is considered. The control is simultaneously applied to both the random and the deterministic components of the system. The noise (the random) term depends on both the states and the control input. The jump Markovian switching is modeled by a discrete-time Markov chain and the noise or stochastic environmental disturbance is modeled by a sequence of identically independently normally distributed random variables. Using linear matrix inequalities (LMIs) approach, the robust quadratic stochastic stability is obtained. The proposed control law for this quadratic stochastic stabilization result depended on the mode of the system. This control law is developed such that the closed-loop system with a cost function has an upper bound under all admissible parameter uncertainties. The upper bound for the cost function is obtained as a minimization problem. Two numerical examples are given to demonstrate the potential of the proposed techniques and obtained results.  相似文献   

15.
This paper extends the notion of generalized joint spectral radius with exponents, originally defined for a finite set of matrices, to probability distributions. We show that, under a certain invariance condition, the radius is calculated as the spectral radius of a matrix that can be easily computed, extending the classical counterpart. Using this result we investigate the mean stability of switching systems. In particular we establish the equivalence of mean square stability, simultaneous contractibility in square mean, and the existence of a quadratic Lyapunov function. Also the stabilization of positive switching systems is studied. Numerical examples are given to illustrate the results.  相似文献   

16.
In this paper, the problem of stability of switched homogeneous systems is addressed. First of all, if there is a quadratic Lyapunov function such that nonlinear homogeneous systems are asymptotically stable, a matrix Lyapunov-like equation is obtained for a stable nonlinear homogeneous system using semi-tensor product of matrices, and Lyapunov equation of linear system is just its particular case. Following the previous results, a sufficient condition is obtained for stability of switched nonlinear homogeneous systems, and a switching law is designed by partition of state space. In particular, a constructive approach is provided to avoid chattering phenomena which is caused by the switching rule. Then for planar switched homogeneous systems, an LMI approach to stability of planar switched homogeneous systems is presented. Similar to the condition for linear systems, the LMI-type condition is easily verifiable. An example is given to illustrate that candidate common Lyapunov function is a key point for design of switching law.  相似文献   

17.
This article is devoted to the problem of robust stabilization of uncertain nonlinear switched systems with canonical structure. It is assumed that the constant parameters of the subsystems are unknown and cannot be adopted in the controller design. In addition, the dynamics of the subsystems are perturbed via modeling errors and external disturbances. The effects of unknown actuator saturation are compensated via proper adaptive control signals. The derived controller is based on the terminal sliding mode theory and does not need any prior knowledge about the bounds of the lumped uncertain terms. It is proved that once the system states reach the prescribed sliding manifold in a finite time interval, the whole system becomes insensitive to both the lumped uncertainties and the switching dynamics of the system. The common assumption of having known quadratic Lyapunov functions for the subsystems is relaxed and the derived adaptive approach does not force any limitation on the switching signal of the system. Subsequently, non-conservative conditions are provided to guarantee the global finite time bounded stability of the equilibrium state for the overall uncertain nonlinear switched system under arbitrary switching signals. A numerical computer simulation demonstrates the robust performance of the proposed controller.  相似文献   

18.
The robust stability for some types of tlme-varying interval raatrices and nonlineartime-varying interval matrices is considered and some sufficient conditions for robust stability of such interval matrices are given, The main results of this paper are only related to the verticesset of a interval matrices, and therefore, can be easily applied to test robust stability of interval matrices. Finally, some examples are given to illustrate the results.  相似文献   

19.
This paper deals with the asymptotic distribution of Wishart matrix and its application to the estimation of the population matrix parameter when the population eigenvalues are block-wise infinitely dispersed. We show that the appropriately normalized eigenvectors and eigenvalues asymptotically generate two Wishart matrices and one normally distributed random matrix, which are mutually independent. For a family of orthogonally equivariant estimators, we calculate the asymptotic risks with respect to the entropy or the quadratic loss function and derive the asymptotically best estimator among the family. We numerically show (1) the convergence in both the distributions and the risks are quick enough for a practical use, (2) the asymptotically best estimator is robust against the deviation of the population eigenvalues from the block-wise infinite dispersion.  相似文献   

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