共查询到20条相似文献，搜索用时 78 毫秒
1.
The parametric H∞ loop shaping technique explores more design flexibility by introducing a free parameter that ensures robust stabilization with regard to normalized coprime factor uncertainty of the shaped plant. This paper addresses a design framework for parametric H∞ loop shaping control using linear matrix inequality (LMI) approach that provides a new set of solvability condition along with the larger feasibility region of solution space over the work of Gu et al. (1999) [6]. An equivalence between the Riccati equation based state-space approach and the proposed LMI framework is established and subsequently, an observer-based structure for parametric H∞ loop shaping controller has been realized. A numerical example is considered to demonstrate the effectiveness of the proposed method and the results therein are compared with the work of Gu et al. (1999) [6]. 相似文献
2.
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
3.
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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This paper is concerned with the global exponential stability for an original class called coupled systems of multi-group neutral delayed differential equations (MNDDEs). By employing Razumikhin method along with graph theory, sufficient conditions are established to guarantee the global exponential stability of MNDDEs, which are in the form of Razumikhin theorem. For the convenience of use, sufficient conditions in the form of coefficients are also obtained. Furthermore, coefficient-type criterion is employed to study the stability of coupled neutral delay oscillators which shows the applicability of our findings. Finally, two numerical examples are given to demonstrate the validity and feasibility of the theoretical results. 相似文献
6.
In this paper, a discrete-time interval general BAM bidirectional associative memory neural networks model is considered. By employing the theory of coincidence degree and using Halanay-type inequality technique we establish new sufficient conditions ensuring the existence and global exponential stability of periodic solutions for the discrete-time interval general BAM bidirectional neural networks. The results obtained generalize and improve known results in [23]. An example is provided to show the correctness of our analysis. 相似文献
7.
In this paper, we consider a predator-prey model with stage-structure and harvesting. This model is the same as the one developed by Kar and Pahari (2007) [9], but we make bifurcation analysis more general than their work. In particular, using the approach of Beretta and Kuang (2002) [4], we show that the positive steady state can be destabilized through a Hopf bifurcation. We also investigate the stability and direction of periodic solutions bifurcating from Hopf bifurcation by using the normal form theory and the center manifold theorem presented in Hassard et al. (1981) [8]. Numerical simulations are then carried out as supporting evidences of our analytical results. 相似文献
8.
《Journal of The Franklin Institute》2023,360(2):1005-1035
There are many hybrid stochastic differential equations (SDEs) in the real-world that don’t satisfy the linear growth condition (namely, SDEs are highly nonlinear), but they have highly nonlinear characteristics. Based on some existing results, the main difficulties here are to deal with those equations if they are driven by Lévy noise and delay terms, then to investigate their stability in this case. The present paper aims to show how to stabilize a given unstable nonlinear hybrid SDEs with Lévy noise by designing delay feedback controls in the both drift and diffusion parts of the given SDEs. The controllers are based on discrete-time state observations which are more realistic and make the cost less in practice. By using the Lyapunov functional method under a set of appropriate assumptions, stability results of the controlled hybrid SDEs are discussed in the sense of pth moment asymptotic stability and exponential stability. As an application, an illustrative example is provided to show the feasibility of our theorem. The results obtained in this paper can be considered as an extension of some conclusions in the stabilization theory. 相似文献
9.
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
10.
《Journal of The Franklin Institute》2022,359(8):3749-3767
This paper investigates practical stability problem for nonlinear impulsive stochastic delayed systems driven by G-Brownian motion (IGSDSs). Practical stability can describe quantitative properties and qualitative behavior in contrast to traditional Lyapunov stability theory. Based on G-Lyapunov function, Razumikhin-type theorem, G-Itô formula, Burkholder–Davis–Gundy (B-D-G) inequalities I & II and stochastic analysis technique, some new criteria for moment and quasi sure global practical uniform exponential stability of IGSDSs are proposed. Finally, two examples are presented to verify validity of our theoretical results. 相似文献
11.
This paper investigates the problem of H∞ filtering for Markovian jump linear systems with time-varying delay. The aim of this problem is to design an H∞ filter that ensures stochastic stability of the filtering error system and a prescribed L2-induced gain from the noise signals to the estimation error, for all admissible uncertainties. For solving the problem, we transform the system under consideration into an interconnection system. Based on the system transformation and the stochastic scaled small gain theorem, stochastic stability of the original system is examined via the stochastic stability version of the bounded realness of the transformed forward system. The merit of the proposed approach lies in its reduced conservatism, which is made possible by a precise approximation of the time-varying delay and the stochastic scaled small gain theorem. The proposed H∞ filtering condition is demonstrated to be less conservative than most existing results. Moreover, the H∞ filter design condition is further presented via convex optimizations, whose effectiveness are also illustrated via numerical examples. 相似文献
12.
In this paper, we consider global adaptive feedback control of nonlinear systems with unknown parameters entering nonlinearly. Such unknown parameters are also not required to lie in a known compact set. Unlike previous results, our proposed adaptive controller is a new double dynamical switching-type controller in which the controller parameter is tuned in a flexible switching manner via a monotonically decreasing switching logic and the controller combines the traditional adaptive theorem with the switching scheme perfectly. Global stability results of the closed-loop system have been proved. 相似文献
13.
Engin H. Copur Ahmet C. Arican Sinan Ozcan Metin U. Salamci 《Journal of The Franklin Institute》2019,356(15):8388-8413
State Dependent Riccati Equation (SDRE) methods have the considerable advantages over other nonlinear control methods. However, stability issues can be arisen in SDRE based control system due to the lack of the global asymptotic stability property. Therefore, the previous studies have usually shown that local asymptotic stability can be ensured by estimating a Region of Attraction (ROA) around the equilibrium point. These estimated regions for stability may become narrow or the condition to keep the states in this region may be very conservative. To resolve these issues, this paper proposes a novel SDRE method employing an update algorithm to re-estimate the ROA when the states tend to move out of the stable region. The tendency is checked using a condition which is developed based on a new theorem. The theorem proves that it is possible to redesign the previous ROA with respect to the current states lying close to its boundary for ensuring the “non-local” stability along the trajectory without the need of solving SDRE at each time instant, unlike the standard SDRE approach. Therefore, the new theorem is now able to enhance the stability of the SDRE based closed-loop control system. The feasibility of the proposed SDRE control method is tested in both simulations and experiments. A validated 3-DOF laboratory helicopter is used for experiments and the control objective for the helicopter is to realise a preplanned movement in both elevation and travel axes. The results reveal that the proposed SDRE approach enables the controlled plant to track the desired trajectory as satisfactorily as the standard SDRE approach, while only solving SDRE when needed. The proposed SDRE method reduces the computational load for practical implementation of the control algorithm whilst ensuring the stability over the operational region. 相似文献
14.
《Journal of The Franklin Institute》2021,358(15):7507-7527
This paper investigates the semi-global cooperative cluster output regulation problem of heterogeneous multi-agent systems with input saturation, the exosystems for each cluster can be different. To avoid using global information (e.g., the minimal nonzero eigenvalue of the Laplacian matrix) in the control protocol, an adaptive dynamic compensator is proposed to estimate exosystem’s state in fully distributed manner. A dynamic event-triggering mechanism with adaptive parameter is proposed in order to reduce the usage of communication resources. Low-gain feedback technique is utilized to deal with the influence of input saturation, and Lypunov-based stability analysis results are obtained. Moreover, it is formally shown that Zeno behavior can be excluded. The superiority of the proposed methods includes: the agents in each cluster are also heterogeneous, which is essentially different from [1]; the event-triggered control strategy does not depend on any global information; and the influence of saturation nonlinearity can be eliminated with low-gain feedback. Finally, a numerical example is provided to illustrate the effectiveness of the proposed methods. 相似文献
15.
We obtain extremal binary self-dual codes of parameters [64,32,12] as binary images of self-dual codes over R1, R2 and R3 by employing different methods. We then apply the extension theorem to these codes to obtain a number of extremal binary self-dual codes of length 66 with trivial automorphism groups. Fifteen of the codes we obtain have new β values in W66,3, of which only three were known to exist before. We also find nine codes with new β values in W66,1, thus updating the list of such known codes. 相似文献
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通过构造V函数法及细致的分析得到系统的一致持续性,在种群一致持续性前提下,利用Brouwer不动点定理证明系统至少存在一个正周期解,并通过构造Lyapunov泛函和运用微分不等式,稳定性理论及Barbalat’s引理得到了判定正周期解的全局渐近稳定性和全局吸引的充分条件。 相似文献
18.
《Journal of The Franklin Institute》2001,338(2-3):187-201
The effects of an added mass on the oscillations of a SDOF bluff body, elastically supported, exposed to a steady flow and undergoing galloping oscillations, are investigated. The stability boundaries of the trivial equilibrium position of the 2DOF system are determined in a four parameters space. The occurrence of different types of bifurcation on these boundaries is highlighted, namely, simple Hopf, non-resonant double Hopf and 1 : 1 resonant double Hopf. The perturbation multiple scale method is employed to analyze the system postcritical behavior around the codimension-1 and codimension-2 critical manifolds. The analytical results are compared with numerical solutions obtained through direct integration of the equations of motion. Finally, the effects of the closeness of the critical frequencies on the non-resonant double Hopf manifold, are discussed by using a quasi-resonant asymptotic solutions. 相似文献
19.
Qiankun Song 《Journal of The Franklin Institute》2008,345(1):39-59
In this paper, the discrete-time fuzzy cellular neural network with variable delays and impulses is considered. Based on M-matrix theory and analytic methods, several simple sufficient conditions checking the global exponential stability and the existence of periodic solutions are obtained for the neural networks. Moreover, the estimation for exponential convergence rate index is proposed. The obtained results show that the stability and periodic solutions still remain under certain impulsive perturbations for the neural network with stable equilibrium point and periodic solutions. Some examples with simulations are given to show the effectiveness of the obtained results. 相似文献
20.
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