共查询到20条相似文献，搜索用时 234 毫秒
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本文考虑一类带有扩散和变时滞的捕食系统,利用微分不等式理论及构造Lyapunov函数的方法,得到系统的一致持久性和全局渐近稳定性的充分条件． 相似文献
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文章研究了一类捕食者具有阶段结构与食饵具有脉冲扰动的捕食系统,并运用脉冲微分方程的理论给出系统捕食者灭绝周期解的全局渐近稳定性。 相似文献
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通过建立Poincar é映射,对一个具有Holling类功能反应函数的捕食者-食饵生物模型在状态脉冲控制下的动力学性质进行了研究,并且得到了一阶周期解及二阶周期解的存在性和稳定性的条件. 相似文献
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研究一种带时滞的基因调控网络(GRN)的全局渐进稳定性证明与推导,引入自组织映射泛函稳定性理论,加入自由权值矩阵,提出通过自组织映射泛函引入辅助矩阵对GRN全局渐进稳定性进行分析证明的方法。在自组织映射泛函中引入了一个新的状态项,包含了一个积分叉积项,提供额外的自由度较少保守性,推导得出GRN系统是全局渐进稳定性的推论。证明结论和得出的推论能有效验证GRN系统的全局渐进稳定性,能得到传统方法不能求解的可行解,相比传统方法更具有一般性和普适性。 相似文献
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研究了控制回路中反馈信号存在的时滞对非线性磁悬浮系统稳定性的影响。运用规范型法和中心流形法,确定出表征磁悬浮时滞系统中Hopf分岔方向、周期解的稳定性及周期变化的特征量,并通过数值模拟验证了主要结果的可靠性。分析表明,当时滞量达到临界值时,系统将会经历一个超临界Hopf分岔而产生稳定的周期振动。 相似文献
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研究具有脉冲出生、脉冲接种和时滞的SEIRS传染病模型,分析无病周期解的存在性和全局稳定性,以及传染病模型的持久性,分析控制传染病传播的主要因素。 相似文献
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史远军 《中国科学院研究生院学报》1997,(1)
在二阶系统一系列定理基础上,建立一个直接根据系统Lyapunov函数性质判定系统周期解存在性的定理,针对一类二阶非自治非线性系统构造了适当的Lyapunov函数,并研究了这类系统周期解的存在性。 相似文献
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Jiayi Liu Shuaihao Jiang Yanbin Qu Xuewei Zhang Huihui Song 《Journal of The Franklin Institute》2021,358(11):5676-5693
In this paper, the global stability of coupled control systems (CCSs) is discussed. Assembling the energy of each vertex system with the help of graph theory, a systematic method for constructing a global Lyapunov function of CCSs is proposed. Then, two kinds of stability criteria by Lyapunov-type theorem and coefficient-type theorem with the condition of the system topology are derived. Subsequently, the theoretical results are applied to the microgrid and the criterion of global asymptotical stability of the microgrid is developed. Meanwhile, based on the actual demand of the microgrid, the secondary frequency distributed consistency sliding mode control of the microgrid is proposed using the consensus algorithm. In the presence of a time-varying load, the control can not only quickly stabilize the frequency at the equilibrium point but also dynamically achieve active power sharing. Finally, the simulation of an islanded microgrid is conducted to test the validity and feasibility of our results. 相似文献
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Yafeng Li Ju H. Park Changchun Hua Qing Geng 《Journal of The Franklin Institute》2021,358(3):1743-1764
In this paper, the global output feedback tracking control is investigated for a class of switched nonlinear systems with time-varying system fault and deferred prescribed performance. The shifting function is introduced to improve the traditional prescribed performance control technique, remove the constraint condition on the initial value, and make the constraint bounds have more alternative forms. To estimate the unmeasured state variables and compensate the system fault, the switched dynamic gain extended state observer is constructed, which relaxes the traditional Lipschitz conditions on the nonlinear functions. Based on the proposed observer, by constructing the new Lyapunov function and using the backstepping method, the global robust output feedback controller is designed to make the output track the reference signal successfully, and after the adjustment time, the tracking error enters into the prescribed set. The stability of the system is analyzed by the average dwell time method. Finally, simulation results are given to illustrate the effectiveness of the proposed method. 相似文献
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Shipei Huang Zhengbing Yan Guoqiang Zeng Zhengjiang Zhang Zhiliang Zhu 《Journal of The Franklin Institute》2019,356(6):3398-3418
This paper investigates the finite-time stabilization for a class of upper-triangular switched nonlinear systems, where nonlinearities are allowed to be lower-order growing. Due to the special structure of the considered system, the presented methods for lower-triangular switched nonlinear systems in the literature can not be directly utilized. To solve the problem, a state feedback control law with a new structure is designed to guarantee the global finite-time stability of the closed-loop system under arbitrary switching signals by using the recursive design approach and the nested saturation method. A simulation example is provided to show the effectiveness of the proposed method. 相似文献
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Memristive models are currently the dominant technique for neuromorphic VLSI design. Critical dynamics research of memristive systems is very meaningful in both theoretical importance and practical significance. In this paper, by using nonsmooth analysis and control theory, nonlinear dynamics on global asymptotic stability and global exponential stability of memristive neural system with unbounded time-varying delays are explored. The theoretical analysis may yield a deep insight into the electric characteristics of memristor devices. 相似文献
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This paper deals with the problem of the global robust asymptotic stability of the class of dynamical neural networks with multiple time delays. We propose a new alternative sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point under parameter uncertainties of the neural system. We first prove the existence and uniqueness of the equilibrium point by using the Homomorphic mapping theorem. Then, by employing a new Lyapunov functional, the Lyapunov stability theorem is used to establish the sufficient condition for the asymptotic stability of the equilibrium point. The obtained condition is independent of time delays and relies on the network parameters of the neural system only. Therefore, the equilibrium and stability properties of the delayed neural network can be easily checked. We also make a detailed comparison between our result and the previous corresponding results derived in the previous literature. This comparison proves that our result is new and improves some of the previously reported robust stability results. Some illustrative numerical examples are given to show the applicability and advantages of our result. 相似文献
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This paper investigates the problem of global stabilization of switched nonlinear systems in non-triangular form whose subsystems are not assumed to be asymptotically stabilizable. The use of multiple Lyapunov functions (MLFs) method permits removal of a common restriction in which the nonlinear structures in the non-switched nonlinear systems are restricted to a triangular structure when applying backstepping. Using the MLFs method and the adding a power integrator technique, we design state-feedback controllers for individual subsystems and construct a switching law to guarantee asymptotic stability of the closed-loop switched system. As an application of the proposed design method, the global stabilization problem of a continuously stirred tank reactor (CSTR) system and two inverted pendulums which cannot be handled by the existing methods is investigated. 相似文献
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By using the Razumikhin-type technique, for stochastic discrete-time delay systems, this paper establishes the discrete Razumikhin-type theorems on the pth moment stability, the global pth moment stability and the pth moment exponential stability, respectively. The almost sure exponential stability is also investigated by using the pth moment exponential stability and the Borel–Cantelli lemma. As the applications of t he established theorems, stability of a special class of stochastic discrete-time delay systems, synchronization of the stochastic discrete-time delay dynamical networks and stabilization of a stochastic discrete-time linear delay time invariant system are examined. 相似文献
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陆征一 《中国科学院研究生院学报》1990,(2)
本文利用单调方法、极位原理、Schauder不动点定理、以及常微系统整体稳定的結论,给出一类带Neumann边值条件的半线性反应扩散系统整体正解的存在唯一性及渐近性. 相似文献
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In this paper, an auxiliary model-based nonsingular M-matrix approach is used to establish the global exponential stability of the zero equilibrium, for a class of discrete-time high-order Cohen–Grossberg neural networks (HOCGNNs) with time-varying delays, connection weights and impulses. A new impulse-free discrete-time HOCGNN with time-varying delays and connection weights is firstly constructed, and the relationship between the solutions of original systems and new HOCGNNs is indicated by a technical lemma. From which, the global exponential stability criteria for the zero equilibrium are derived by using an inductive idea and the properties of nonsingular M-matrices. The effectiveness of the obtained stability criteria is illustrated by numerical examples. Compared with the previous results, this paper has three advantages: (i) The Lyapunov–Krasovskii functional is not required; (ii) The obtained global exponential stability criteria are applied to check whether a matrix is a nonsingular M-matrix, which can be conveniently tested; (iii) The proposed approach applies to most of discrete-time system models with impulses and delays. 相似文献
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《Journal of The Franklin Institute》2022,359(10):4893-4914
This paper investigates the global stabilization of discrete-time linear systems with input time delay by bounded controls. Based on some special canonical forms containing time delays both in its input and state, two special discrete-time linear systems---multiple integrators and oscillators are first considered. The global stabilizing controllers are respectively established, and moreover, explicit conditions are established to guarantee the stability of the closed-loop systems. Subsequently, a concise design method is proposed for globally stabilizing general discrete-time linear system by combining the design methods for multiple integrators and oscillators. The designed controller is in the explicit form with explicit stability conditions being given, and thus is easier to use than the existing results. Finally, numerical simulations illustrate the effectiveness of the proposed approaches. 相似文献