共查询到19条相似文献,搜索用时 343 毫秒
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陀螺仪是一个非常有趣,又是永恒的非线性非自治动力系统课题,它可以显示出非常复杂的动力学行为,如混沌现象.在一个给定的有限时间内,研究非线性非自治陀螺仪鲁棒稳定性问题.假设陀螺仪系统受到模型不确定的外部扰动而摄动,系统参数并不知道,同时考虑了非线性输入的影响.为未知参数提出了适当的自适应律.以自适应律和有限时间控制理论为基础,提出非连续有限时间控制理论,来研究系统的有限时间稳定性.解析证明了闭循环系统的有限时间稳定性及其收敛性.若干数值仿真结果表明,该文的有限时间控制法是有效的,同时验证了该文的理论结果. 相似文献
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文[1]研究了带有一个非自治项的四阶微分方程的全局稳定性,它推广了[2]的结果。本文研究一般的四阶非自治微分方程 (1)的全局渐近稳定性。对这个方程,我们构造了所需要的函数,并参照文[3][4]的办法,作出了易于检验的判定四阶非自治系统全局渐近稳定的充分条件。 相似文献
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一类非自治系统的稳定性 总被引:3,自引:0,他引:3
骆桦 《数学的实践与认识》2005,35(2):169-171
通过构造 Liapunov函数给出了一类非自治系统的稳定性的判定准则 .并给出了其有关的应用实例 相似文献
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The horizontal platform system (HPS) is a mechanical device that exhibits rich and chaotic dynamics. In this paper, the problem of finite-time synchronization of two non-autonomous chaotic HPSs is investigated. It is assumed that both drive and response systems are disturbed by model uncertainties, external disturbances and fully unknown parameters. Appropriate update laws are proposed to undertake the unknown parameters. Using the update laws and finite-time control theory, a robust adaptive controller is derived to synchronize the two uncertain HPSs in a given finite time. Subsequently, the effects of input nonlinearities are taken into account and a robust adaptive controller is introduced to synchronize the two uncertain HPSs within a finite time. The finite-time stability and convergence of the proposed schemes are analytically proved. Two illustrative examples are presented to show the robustness and applicability of the proposed adaptive finite-time control techniques. 相似文献
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This paper deals with the problem of finite-time stability and stabilization of nonlinear Markovian switching stochastic systems which exist impulses at the switching instants. Using multiple Lyapunov function theory, a sufficient condition is established for finite-time stability of the underlying systems. Furthermore, based on the state partition of continuous parts of systems, a feedback controller is designed such that the corresponding impulsive stochastic closed-loop systems are finite-time stochastically stable. A numerical example is presented to illustrate the effectiveness of the proposed method. 相似文献
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Oleg Makarenkov 《Comptes Rendus Mathematique》2017,355(3):277-281
We offer a simple proof of the Lyapunov finite-time stability theorem for Filippov systems which does not use any generalized derivatives to differentiate the composition of the Lyapunov function with absolutely continuous solutions. 相似文献
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讨论随机系统的有限时间镇定问题.首先提出了随机系统有限时间稳定的概念;其次证明了随机系统有限时间稳定的Lyapunov定理;然后,讨论了一类随机系统的镇定问题. 相似文献
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《Nonlinear Analysis: Hybrid Systems》2008,2(3):832-845
Finite-time stability involves dynamical systems whose trajectories converge to a Lyapunov stable equilibrium state in finite time. For continuous-time dynamical systems finite-time convergence implies nonuniqueness of system solutions in reverse time, and hence, such systems possess non-Lipschitzian dynamics. For impulsive dynamical systems, however, it may be possible to reset the system states to an equilibrium state achieving finite-time convergence without requiring non-Lipschitzian system dynamics. In this paper, we develop sufficient conditions for finite-time stability of impulsive dynamical systems using both scalar and vector Lyapunov functions. Furthermore, we design hybrid finite-time stabilizing controllers for impulsive dynamical systems that are robust against full modelling uncertainty. Finally, we present a numerical example for finite-time stabilization of large-scale impulsive dynamical systems. 相似文献
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Robustness of stability with respect to small delays, e.g., motivated by feedback systems in control theory, is of great theoretical and practical important, but this property does not hold for many systems. In this paper, we introduce the conception of robustness with respect to small time-varying delays for exponential stability of the non-autonomous linear systems. Sufficient conditions are given for the non-autonomous systems to be robust, and examples are provided to illustrate that the conditions are satisfied for a large class of the non-autonomous parabolic systems. 相似文献
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非线性非定常系统的稳定性 总被引:1,自引:0,他引:1
本文研究一般情形的非线性非定常系统的稳定性,给出了一个广泛而又实用指数稳定性定理。即使是线性时变系统的情形,我们的结果也具一般性,且有应用方便,简捷等优点。 相似文献
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Sergey P. Kuznetsov 《Communications in Nonlinear Science & Numerical Simulation》2009,14(9-10):3487-3491
A non-autonomous flow system is introduced with an attractor of Plykin type that may serve as a base for elaboration of real systems and devices demonstrating the structurally stable chaotic dynamics. The starting point is a map on a two-dimensional sphere, consisting of four stages of continuous geometrically evident transformations. The computations indicate that in a certain parameter range the map has a uniformly hyperbolic attractor. It may be represented on a plane by means of a stereographic projection. Accounting structural stability, a modification of the model is undertaken to obtain a set of two non-autonomous differential equations of the first order with smooth coefficients. As follows from computations, it has the Plykin type attractor in the Poincaré cross-section. 相似文献
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The hybrid systems with continuous and discrete variables can be used to describe many real-world phenomena. In this paper, by generalizing the mathematical form of gene regulatory networks, a novel class of hybrid systems consisting of continuous and Boolean dynamics is investigated. Firstly, the new hybrid system is introduced in detail, and a concept of finite-time stability (FTS) for it is proposed. Next, the existence and uniqueness of solutions are proved by fixed point theory. Furthermore, based on Lyapunov functions and the semi-tensor product (STP), i.e., Cheng product, some sufficient conditions of FTS for the hybrid systems are presented. The main results are illustrated by two numerical examples. 相似文献