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1.
This paper investigates the problem for stability of neutral-type dynamical neural networks involving delay parameters. Different form the previously reported results, the states of the neurons involve multiple delays and time derivative of states of neurons include discrete time delays. The stability of such neural systems has not been given much attention in the past literature due to the difficulty of finding Lyapunov functionals which are suitable for stability analysis of this type of neural networks. This paper constructs a generalized Lyapunov functional by introducing new terms into the well-known Lyapunov functional that enables us to conduct a theoretical investigation into stability analysis of delayed neutral-type neural systems. Based on this modified novel Lyapunov functional, sufficient criteria are derived, which guarantee the existence, uniqueness and global asymptotic stability of the equilibrium point of the neutral-type neural networks with multiple delays in the states and discrete delays in the time derivative of the states. The applicability of the proposed stability conditions rely on testing two basic matrix properties. The constraints impose on the system matrices are determined by using nonsingular M-matrix condition, and the constraints imposed on the coefficients of the time derivative of the delayed state variables are derived by exploiting the vector-matrix norms. We also note that the obtained stability conditions have no involvement with the delay parameters and expressed in terms of nonlinear Lipschitz activation functions. We present a constructive numerical example for this class of neural networks to give a systematic procedure for determining the imposed conditions on the whole system parameters of the delayed neutral-type neural systems.  相似文献   

2.
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3.
This paper is concerned with the stability analysis of discrete-time linear systems with time-varying delays. The novelty of this paper lies in that a novel Lyapunov–Krasovskii functional that updates periodically along with the time is proposed to reduce the conservatism and eventually be able to achieve the non-conservativeness in stability analysis. It can be proved that the stability of a discrete-time linear delay system is equivalent to the existence of a periodic Lyapunov–Krasovskii functional. Two necessary and sufficient stability conditions in terms of linear matrix inequalities are proposed in this paper. Furthermore, the novel periodic Lyapunov–Krasovskii functional is employed to solve the ?2-gain performance analysis problem when exogenous disturbance is considered. The effectiveness of the proposed results is illustrated by several numerical examples.  相似文献   

4.
This paper investigates the stability of linear control systems with aperiodic sampled data and communication delays. A systematic analysis method is presented and then it is applied to an electric power market. Firstly, the sampled-data system is transformed into a system with a special time-varying delay via the input delay method. Secondly, a less conservative stability criterion is derived based on Lyapunov theory. Several augmented terms and an extra integral term are introduced during the constructing of candidate Lyapunov–Krasovskii functional (LKF); and an improved free-weighting matrix approach is used to handle with the LKF itself and its derivative for obtaining the relaxed conditions ensuring the positive and decreasing requirements of the LKF. The benefit of those treatments on the conservativeness-reducing is analyzed and verified based on a simple numerical example. Finally, the application of the proposed method to a simplified electric power market is investigated, including modeling the system with market clearing time and communication delay, and determining the stability region. The application also shows the practical significance of the reducing of the conservativeness.  相似文献   

5.
In this paper, a hybrid triple delayed prey predator bioeconomic system with prey refuge and Lévy jumps is established, where both maturation delay for prey and predator population and gestation delay for predator population are considered. For deterministic system, positivity and uniform permanence of solution are discussed. Local stability of deterministic system around interior equilibrium is investigated due to variations of triple time delays. For stochastic system without time delay, sufficient conditions for stochastically ultimate boundedness and stochastic permanence are discussed. Existence of stochastic Hopf bifurcation and stochastic stability are investigated. For stochastic system with triple time delays, existence and uniqueness of global positive solution are studied. Finally, combined dynamic effects of triple time delays and Lévy jumps on the hybrid stochastic system are discussed by constructing appropriate Lyapunov functions. Numerical simulations are supported to illustrate theoretical analysis.  相似文献   

6.
This paper investigates the problem of observer-based decentralized control for a class of large-scale stochastic high-order feedforward systems with multi time delays. By using the homogeneous domination idea and constructing the implementable observer, the decentralized output-feedback controller design scheme is firstly proposed. Then, with the aid of stochastic time delay system stability theory, the globally asymptotically stable in probability of the closed-loop system is verified by selecting an appropriate Lyapunov–Krasoviskii functional. Finally, an example is provided to demonstrate the efficiency of the proposed design method.  相似文献   

7.
This paper deals with the problem of stabilization for a class of hybrid systems with time-varying delays. The system to be considered is with nonlinear perturbation and the delay is time varying in both the state and control. Using an improved Lyapunov–Krasovskii functional combined with Newton–Leibniz formula, a memoryless switched controller design for exponential stabilization of switched systems is proposed. The conditions for the exponential stabilization are presented in terms of the solution of matrix Riccati equations, which allow for an arbitrary prescribed stability degree.  相似文献   

8.
In this paper, we discussed the robust finite-time stability of conic type nonlinear systems with time varying delays. Some novel conditions are derived to design a linear quadratic regulator (LQR) based sliding mode control (SMC) by proposing an integral switching surface. The sufficient conditions are derived for the considered nonlinear system using Lyapunov–Krasovskii stability theory and linear matrix inequality (LMI) approach. The proposed conditions can be solved using some standard numerical packages. Finally, a practical example is provided to validate the advantages and effectiveness of the proposed results.  相似文献   

9.
In this paper, the problem of stability analysis for linear systems with time-varying delays is considered. By the consideration of new augmented Lyapunov functionals, improved delay-dependent stability criteria for asymptotic stability of the system are proposed for two cases of conditions on time-varying delays with the framework of linear matrix inequalities (LMIs), which can be solved easily by various efficient convex optimization algorithms. The enhancement of the feasible region of the proposed criteria is shown via three numerical examples by the comparison of maximum delay bounds.  相似文献   

10.
In this paper, we will give necessary conditions for the exponential stability of linear neutral type systems with multiple time delays by employing the Lyapunov–Krasovskii functional approach. These conditions not only extend the existing results of the neutral-delay-free systems, but also provide a new tool for stability analysis of linear neutral type systems with multiple time delays by characterizing instability domains. As a medium step, we will investigate several crucial properties which are involved with both the fundamental matrix and Lyapunov matrix. Numerical examples illustrate the validity of the theoretical results.  相似文献   

11.
In this paper, we will investigate the necessary conditions, described by the Lyapunov matrix, for the robust exponential stability for a class of linear uncertain systems with a single constant delay and time-invariant parametric uncertainties, which are some generalizations of the existing results on uncertain linear time-delay systems. As a medium step, several pivotal properties of parameter-dependent Lyapunov matrix are proposed, which set up the relationships between fundamental matrix and Lyapunov matrix for the considered system. In addition, to calculate the parameter-dependent Lyapunov matrix, we introduce the differential equation method and the Lagrange interpolation method, respectively. Furthermore, it is noted that the proposed necessary conditions can be used to estimate the range of time delay, when the linear uncertain time-delay system is robust exponential stability. Finally, the validity of the obtained theoretical results is illustrated via numerical examples.  相似文献   

12.
基于参数相关Lyapunov泛函不确定时滞系统的鲁棒稳定性   总被引：3，自引：0，他引：3  
研究了含多面体不确定性的时滞系统的鲁棒稳定性问题。利用参数相关的Lyapunov泛函,得到了基于LMI的时滞系统时滞相关的鲁棒稳定的充分条件。在该条件中不确定系统在多面体不同的顶点用不同的Lyapunov阵判断其稳定性,而已有的结果为在所有的顶点用一个共同Lyapunov阵分析。进一步,将确定系统稳定的最大时滞问题转化为求广义特征值的拟凸优化问题。最后数值例子说明了该方法有较小的保守性  相似文献   

13.
This paper proposes a fuzzy model predictive control (FMPC) combined with the modified Smith predictor for networked control systems (NCSs). The network delays and data dropouts are problems, which greatly reduce the controller performance. For the proposed controller, the model of the controlled system is identified on-line using the Takagi – Sugeno (T-S) fuzzy models based on the Lyapunov function. There are two internal loops in the proposed structure. The first is the loop around the FMPC, which predicts the future outputs. The other is the loop around the plant to give the error between the system model and the actual plant. The proposed controller is designed for controlling a DC servo system through a wireless network to improve the system response. The practical results based on MATLAB/SIMULINK are established. The practical results are indicated that the proposed controller is able to respond the networked time delay and data dropouts compared to other controllers.  相似文献   

14.
This paper is concerned with the stability analysis of systems with two additive time-varying delay components in an improved delay interconnection Lyapunov–Krasovskii framework. At first, an augmented vector and some integral terms considering the additive delays information in a new way are introduced to the Lyapunov–Krasovskii functional (LKF), in which the information of the two upper bounds and the relationship between the two upper bounds and the upper bound of the total delay are both fully considered. Then, the obtained stability criterion shows advantage over the existing ones since not only an improved delay interconnection LKF is constructed but also some advanced techniques such as the free-matrix-based integral inequality and extended reciprocally convex matrix inequality are used to estimate the upper bound of the derivative of the proposed LKF. Finally, a numerical example is given to demonstrate the effectiveness and to show the superiority of the proposed method over existing results.  相似文献   

15.
This paper studies the problems of stability and H∞ model reference tracking performance for a class of asynchronous switched nonlinear systems with uncertain input delay. First, it is assumed switched controller and corresponding piecewise Lyapunov function are unknown but the derivative of piecewise Lyapunov function has a condition; this condition implies that the nominal system (system without input delay and disturbance) is exponentially stable by any switched controller which satisfies this condition. With this assumption, a proper Lyapunov–Krasovskii functional is constructed. By employing this new functional and average dwell time technique, the delay-dependent input-to-state stability criteria are derived under a certain delay bound; in addition, a mechanism which finds the upper bound of input delay is proposed. Finally, a kind of state feedback control law which fulfils condition of aforesaid piecewise Lyapunov function is introduced to guarantee the input-to-state stability and H∞ model reference tracking performance. Simulation examples are presented to demonstrate the efficacy of results.  相似文献   

16.
This paper deals with stability of discrete-time systems with an interval-like time-varying delay. By constructing a novel augmented Lyapunov functional and using an improved finite-sum inequality to deal with some sum-terms appearing in the forward difference of the Lyapunov functional, a less conservative stability criterion is obtained for the system under study if compared with some existing methods. Moreover, as a special case, the stability of discrete-time systems with a constant time delay is also investigated. Three numerical examples show that the derived stability criteria are less conservative and require relatively small number of decision variables.  相似文献   

17.
This paper studies the exponential stability of switched positive system consisting of unstable subsystems with distributed time-varying delay. Unlike the existing results concerning delays, switching behaviors dominating the system can be either stabilizing or destabilizing. The distributed delay is supposed to be slowly varying and upper-bounded. To tackle the difficulties brought by both the switching behaviors with mixed effects and the distributed delay, a multiple discretized Lyapunov–Krasovskii functional is employed to derive sufficient conditions for the exponential stability of the system. Specifically, by adjusting the ratio of the stabilizing switching behaviors, the state divergence caused by unstable subsystems and destabilizing switching behaviors can be compensated. Simulation examples demonstrate the effectiveness of the results.  相似文献   

18.
This paper investigates the problem of global exponential stability for neutral systems with interval time varying delays and nonlinear perturbations. It is assumed that the state delay belongs to a given interval, which means that both the lower and upper bounds of the time-varying delay are available. The uncertainties under consideration are norm-bounded. Based on the Lyapunov–Krasovskii stability theory, delay-partitioning technique and lower bounds lemma, less conservative delay-dependent exponential stability criteria are derived in terms of linear matrix inequalities (LMIs) with fewer decision variables than the existing ones. Numerical examples are given to show the effectiveness of the proposed method.  相似文献   

19.
This paper presents novel approaches for stability analysis of switched linear time-delay stochastic systems under dwell time constraint. Instead of using comparison principle, piecewise switching-time-dependent discretized Lyapunov functions/functionals are introduced to analyze the stability of switched stochastic systems with constant or time-varying delays. These Lyapunov functions/functionals are decreasing during the dwell time and non-increasing at switching instants, which lead to two mode-dependent dwell-time-based delay-independent stability criteria for the switched systems without restricting the stability of the subsystems. Comparison and numerical examples are provided to show the efficiency of the proposed results.  相似文献   

20.
This paper improves stability criteria for neutral-type Lur’e systems with time-varying delays, where the nonlinearity satisfies sector and slope restrictions. A proposed Lyapunov–Krasovskii functional consisting of a quadratic term and integral terms for the time-varying delays and the nonlinearities, has four different characteristics. First, the quadratic term utilizes not only the current and delayed states but also the nonlinear vectors. Second, the integral terms for nonlinearities fully exploit the characteristics of sector and slope restrictions. Third, the integral terms for nonlinearities also exploit the characteristic of incremental restriction induced from the slope restriction. Fourth, this paper utilizes a vector related to the time derivative of the neutral delayed state to handle the neutral delay. Based on the proposed Lyapunov–Krasovskii functional, the improved stability criteria are derived in terms of linear matrix inequalities. Numerical examples show that the proposed criteria present less conservative results than the previous criteria.  相似文献   

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