共查询到10条相似文献,搜索用时 484 毫秒
1.
线性Volterra系统V泛函的构造及其应用 总被引:1,自引:0,他引:1
V泛函的构造是讨论Volterra积分微分系统稳定性的关键.近十年来,不少作者在Liapunov泛函构造方面作了不少努力,但对一般的线性Volterra系统,还是没有构造Lispunov泛函通用而有效的方法.本文通过具体求解一个线性偏微分方程的方法来确定V泛函,得到了更广泛的Liapunov泛函以及变号V泛函.同时,利用这些V泛函对线性Volterra系统的实用稳定性与Lispunov稳定性作了讨论. 相似文献
2.
Under consideration is the problem of stability of switched discrete systems with the generalized homogeneous right-hand sides. The conditions are obtained for the existence of the common Lyapunov function, and a method for its construction is proposed in the form of a combination of the partial Lyapunov functions obtained for isolated subsystems. For a special case of linear three-dimensional systems, some algorithms are proposed for constructing common Lyapunov functions as quadratic and fourth degree forms. Some examples illustrate the effectiveness of the proposed approach. 相似文献
3.
D. H. Korenivs’kyi 《Ukrainian Mathematical Journal》2005,57(12):2021-2026
We describe the destabilizing (in the sense of a decrease in the reserve of mean-square asymptotic stability) effect of random
parametric perturbations of the white-noise type in quasilinear continuous and discrete dynamical systems (Lur’e-Postnikov
systems of automatic control with nonlinear feedback). We use stochastic Lyapunov functions in the form of linear combinations
of the types “a quadratic form of phase coordinates plus the integral of a nonlinearity” (continuous systems) and “a quadratic
form of phase coordinates plus the integral sum for a nonlinearity” (discrete systems) and the matrix algebraic Sylvester
equations associated with stochastic Lyapunov functions of this form.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 12, pp. 1719–1724, December, 2005. 相似文献
4.
一类离散的时滞脉冲切换系统的H_∞二次稳定性 总被引:1,自引:0,他引:1
研究了一类离散的时滞脉冲切换系统的H_∞控制问题,利用Lyapunov稳定性理论和线性矩阵不等式方法,给出了离散脉冲切换系统具有性能指标γ的充分条件. 相似文献
5.
一类四阶非线性系统的李雅普诺夫函数构造和零解稳定性 总被引:4,自引:0,他引:4
计算出了四阶常系数线性系统的各种形式的李雅普诺夫函数,并将四阶非线性系统化成它的等价系统,通过类比的方法构造出一类四阶非线性系统的李雅普诺夫函数,从而获得该系统零解全局渐近稳定的充分条件. 相似文献
6.
We consider dynamic systems which evolve on discrete time domains where the time steps form a sequence of independent, identically distributed random variables. In particular, we classify the mean-square stability of linear systems on these time domains using quadratic Lyapunov functionals. In the case where the system matrix is a function of the time step, our results agree with and generalize stability results found in the Markov jump linear systems literature. In the case where the system matrix is constant, our results generalize, illuminate, and extend to the stochastic realm results in the field of dynamic equations on time scales. In order to help see the factors that contribute to stability, we prove a sufficient condition for the solvability of the Lyapunov equation by appealing to a fixed point theorem of Ran and Reurings. Finally, an example using observer-based feedback control is presented to demonstrate the utility of the results to control engineers who cannot guarantee uniform timing of the system. 相似文献
7.
V. M. Kuntsevich 《Proceedings of the Steklov Institute of Mathematics》2006,255(2):S93-S102
On the basis of sufficient condition of the stability of linear nonstationary discrete systems stated in this paper, we carry out an analysis of stability for a special class of discrete systems with nonstationary linear part, whose parameters satisfy constraints in the form of sets, and with a scalar nonlinear function satisfying linear or nonlinear restrictions. The problem of parametric synthesis of robustly stable control systems is solved for the same class of objects. The obtained results are generalized to the class of nonstationary systems with many nonlinearities of the same type. 相似文献
8.
9.
S.Abu el Ata-Doss 《Journal of Mathematical Analysis and Applications》1979,72(1):106-113
Control systems governed by linear parabolic evolution partial differential equations in the case of quadratic cost functions are considered. Sensitivity of the performance of the optimal systems to small parameter variations is studied. It is proved that the cost function sensitivity is the same if the optimal control is implemented in open-loop form or in feedbeck form. 相似文献
10.
本利用李雅普诺夫第二方法,对常系数线性系统给出了一类不稳定的简明判别准则,该准则依据A(aij)本身元素aji之间的代数递推公式演算,并可用计算机的循环程序予以实现。 相似文献