Robust stability results for uncertain stochastic neural networks with discrete interval and distributed time-varying delays

This Letter is concerned with stability analysis problem for uncertain stochastic neural networks with discrete interval and distributed time-varying delays. The parameter uncertainties are assumed to be norm bounded and the delay is assumed to be time-varying and belong to a given interval, which means that the lower and upper bounds of interval time-varying delays are available. Based on the Lyapunov-Krasovskii functional and stochastic stability theory, delay-interval dependent stability criteria are obtained in terms of linear matrix inequalities. Some stability criteria are formulated by means of the feasibility of a linear matrix inequality (LMI) and by introducing some free-weighting matrices. Finally, two numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI conditions.     

Robust μ -stability for uncertain stochastic neural networks with unbounded time-varying delays

In this paper, we investigate the global robust stability for uncertain stochastic neural networks with unbounded time-varying delays and norm-bounded parameter uncertainties. A new concept of global robust μ-stability in the mean square for neural networks is given first, then by means of the linear matrix inequality (LMI) approach, stability criteria are presented. Several corollaries are also derived. A simple example is presented to demonstrate the effectiveness of the main result.     

Actuator saturation control of uncertain structures with input time delay

This paper presents a robust saturation control approach for active vibration attenuation of building structures involving parameter uncertainties and input time delay. The parameter uncertainties are described in both polytopic and norm-bounded forms and represent the variations of floor masses, stiffnesses and damping coefficients. The input time delay can be time-varying within a known bound. In terms of the feasibility of certain delay-dependent linear matrix inequalities (LMIs), a state feedback controller can be designed to guarantee the robust stability and performance of the closed-loop system in the presence of parameter uncertainties, actuator saturation, and input time delay. The effectiveness of the proposed approach is investigated by numerical simulations on the vibration control of a three-storey building structure subject to seismic excitation. It is validated that the designed robust saturation controller can effectively suppress the structural vibration and keep the system stability when there are parameter uncertainties and input time delay.     

Stability analysis of impulsive stochastic Cohen-Grossberg neural networks with mixed time delays

In this paper, the problem of stability analysis for a class of impulsive stochastic Cohen-Grossberg neural networks with mixed delays is considered. The mixed time delays comprise both the time-varying and infinite distributed delays. By employing a combination of the M-matrix theory and stochastic analysis technique, a sufficient condition is obtained to ensure the existence, uniqueness, and exponential p-stability of the equilibrium point for the addressed impulsive stochastic Cohen-Grossberg neural network with mixed delays. The proposed method, which does not make use of the Lyapunov functional, is shown to be simple yet effective for analyzing the stability of impulsive or stochastic neural networks with variable and/or distributed delays. We then extend our main results to the case where the parameters contain interval uncertainties. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. An example is given to show the effectiveness of the obtained results.     

Adaptive input-to-state stable synchronization for uncertain time-delay Lur'e systems

This paper is dedicated to the study of adaptive input-to-state stable synchronization of uncertain time-delay Lur'e systems with exterior interference. With the help of the Lyapunov function approach, a sufficient condition for the input-to-state stability of the synchronization-error system is derived, which is theoretically less conservative than a previously reported criterion in the absence of parameter uncertainties. On the basis of the present condition, a co-design of the feedback gain and estimates of the uncertain parameters is given to determine the desired adaptive synchronization controller. Finally, an example with simulations is provided to demonstrate the applicability and superiority of the analysis and design strategies.     

Exponential stability of delayed Hopfield neural networks with various activation functions and polytopic uncertainties

This Letter deals with the problem of exponential stability for a class of delayed Hopfield neural networks. Based on augmented parameter-dependent Lyapunov-Krasovskii functionals, new delay-dependent conditions for the global exponential stability are obtained for two cases of time-varying delays: the delays are differentiable and have an upper bound of the delay-derivatives, and the delays are bounded but not necessary to be differentiable. The conditions are presented in terms of linear matrix inequalities, which allow to compute simultaneously two bounds that characterize the exponential stability rate of the solution. Numerical examples are included to illustrate the effectiveness of our results.     

Vibration suppression in belt-driven servo systems containing uncertain nonlinear dynamics

This paper proposes a vibration suppression strategy for belt-driven servo systems subject to uncertain nonlinear dynamics and external disturbances. The function approximation technique is applied to estimate the uncertainties that are further covered by sliding-based design. The closed loop stability is justified with Lyapunov-like method to ensure ultimately uniformly bounded performance of the output error. Simulation cases show that the proposed strategy can stabilize the closed loop system with effective suppression of vibration regardless of various uncertain nonlinear dynamics and external disturbances.     

非匹配不确定交叉严反馈超混沌系统神经网络反演同步

针对一类具有非匹配不确定性的交叉严反馈超混沌系统,提出一种基于多层前向神经网络的反演自适应同步设计方法.利用神经网络估计系统中的不确定性,运用滑模控制和交叉自适应反演控制处理系统中的非匹配不确定性及神经网络的逼近误差, 当虚拟控制项系数不过零时可保证系统的同步误差趋向于零,过零时可保证同步误差有界. 数值仿真证明了提出的控制方案的有效性.     

Finite time decentralized event-triggered communication scheme for neutral-type Markovian jump neural networks with time varying delays

The objective of this paper is to analyze the finite time problem of a class of neutral-type Markovian jump neural networks with time varying delays and parametric uncertainties using decentralized event-triggered communication scheme. We present a methodology for designing decentralized event-triggered, which utilize only locally available information, for determining the time instants of transmission from the sensors to the central controller. Based on the Lyapunov function with inequality techniques like reciprocal convex combination method, some sufficient conditions are derived to guarantee the finite-time stability of the considered neural networks. Furthermore, the decentralized event-triggered scheme combined with state feedback controller and is designed to solve the finite time stability. The obtained stability criteria are stated in terms of linear matrix inequalities (LMIs), which can be checked numerically using the effective LMI toolbox in MATLAB. Finally, numerical examples are given to illustrate the effectiveness and reduced conservatism of the proposed results over the existing ones.     

Stochastic stability of uncertain Hopfield neural networks with discrete and distributed delays

This Letter is concerned with the global asymptotic stability analysis problem for a class of uncertain stochastic Hopfield neural networks with discrete and distributed time-delays. By utilizing a Lyapunov–Krasovskii functional, using the well-known S-procedure and conducting stochastic analysis, we show that the addressed neural networks are robustly, globally, asymptotically stable if a convex optimization problem is feasible. Then, the stability criteria are derived in terms of linear matrix inequalities (LMIs), which can be effectively solved by some standard numerical packages. The main results are also extended to the multiple time-delay case. Two numerical examples are given to demonstrate the usefulness of the proposed global stability condition.     

基于粒子群优化的自适应模糊制冷控制算法

为解决空间斯特林制冷机和探测器热负载不确定及存在变化的问题,提出了自适应模糊PID制冷控制。在空间环境中使用的斯特林制冷机参数会随着时间的变化而发生改变,探测器负载也会随着工作模式和工作时间的变化而变化,整个制冷系统涉及的变量多,参数非线性。采用传统的控制方法,在固定的单一条件、环境下得到的控制参数,环境和负载发生变化后容易性能变差甚至不稳定,控制精度和稳定性不能满足使用要求。设计了一种自适应斯特林制冷机控制器,通过综合自适应模糊PID控制的方法,采用粒子群优化算法调整控制参数以减小代价函数。通过仿真和试验验证算法的有效性和鲁棒性。     

Adaptive State Estimation for a Class of Nonlinear Stochastic Systems under Generalized Lipschitz Condition

This paper is concerned with adaptive observer design problem for a class of nonlinear stochastic systems. Unknown constant parameters are assumed to be norm bounded. In order to better use the structural knowledge of the nonlinear part, a generalized Lipschitz condition is introduced to the adaptive observer design for a class of nonlinear stochastic systems for the first time. Based on a Lyapunov-Krasovskii functional approach and stochastic Lyapunov stability theory, we present a new adaptive observer design condition with ultimately exponentially bounded in sense of mean square for errors systems in terms of linear matrix inequality (LMI). A numerical example is exploited to show the validity and feasibility of the results.     

Robust impulsive synchronization of coupled delayed neural networks with uncertainties

This paper investigates the synchronization scheme of coupled neural networks with time delays. The coupling function, which can be linear or nonlinear, is subject to uncertainties in the network. By utilizing the stability theory for impulsive functional differential equations, several new criteria are obtained to ensure the robust synchronization of coupled networks via impulsive control. Furthermore, an estimation of the predicted stable region is derived to facilitate the design of the control gain. Finally, numerical simulations are presented to demonstrate the effectiveness of our results.     

Stochastic stability of genetic regulatory networks with a finite set delay characterization

In this paper, the delay-distribution-dependent stability is derived for the stochastic genetic regulatory networks (GRNs) with a finite set delay characterization and interval parameter uncertainties. One important feature of the obtained results here is that the time-varying delays are assumed to be random and the sum of the occurrence probabilities of the delays is assumed to be 1. By employing a new Lyapunov-Krasovskii functional dependent on auxiliary delay parameters which allow the time-varying delays to be not differentiable, less conservative mean-square stochastic stability criteria are obtained. Finally, two examples are given to illustrate the effectiveness and superiority of the derived results.     

An analysis of global robust stability of neural networks with discrete time delays

This Letter presents a new sufficient condition for the existence, uniqueness and global robust asymptotic stability of the equilibrium point for neural networks with discrete time delays. The obtained condition can be easily verified as it is in terms of the network parameters only. Some numerical examples are given to compare our results with previous robust stability results derived in the literature.     

Impulsive control for permanent magnet synchronous motors with uncertainties: LMI approach

A permanent magnet synchronous motor (PMSM) may have chaotic behaviours under certain working conditions, especially for uncertain values of parameters, which threatens the security and stability of motor-driven operation. Hence, it is important to study methods of controlling or suppressing chaos in PMSMs. In this paper, the stability of a PMSM with parameter uncertainties is investigated. After uncertain matrices which represent the variable system parameters are formulated through matrix analysis, a novel asymptotical stability criterion is established by employing the method of Lyapunov functions and linear matrix inequality technology. An example is also given to illustrate the effectiveness of our results.     

Stochastic finite-time stability of reaction-diffusion Cohen–Grossberg neural networks with time-varying delays

This paper investigates the problem of the stochastic finite-time stability of reaction-diffusion Cohen-Grossberg neural networks with time varying delays using the Dirichlet boundary condition. The concept of finite-time stability for the system is first derived by using the stochastic conditions. By constructing a new Lyapunov–Krasovskii functional and utilizing Jensen’s inequality, Wirtinger’s type inequality technique, the Gronwall inequality and the linear matrix inequality (LMI) frame work, conditions are obtained which guarantee the stochastically finite-time stability of Cohen–Grossberg neural networks. Finally, two numerical examples are given to show the effectiveness of the proposed results.     

New Stability Criteria for High-Order Neural Networks with Proportional Delays

This paper is concerned with high-order neural networks with proportional delays. The proportional delay is a time-varying unbounded delay which is different from the constant delay, bounded time-varying delay and distributed delay. By the nonlinear transformation yi(t) = ui( et)(i = 1, 2,..., n), we transform a class of high-order neural networks with proportional delays into a class of high-order neural networks with constant delays and timevarying coefficients. With the aid of Brouwer fixed point theorem and constructing the delay differential inequality, we obtain some delay-independent and delay-dependent sufficient conditions to ensure the existence, uniqueness and global exponential stability of equilibrium of the network. Two examples with their simulations are given to illustrate the theoretical findings. Our results are new and complement previously known results.     

Global Lagrange stability for neutral-type inertial neural networks with discrete and distributed time delays

This paper focus on the problem of global Lagrange stability for neutral-type inertial neural networks with discrete and distributed time delays. By choosing a proper variable substitution, an inertial neural network consisting of second-order differential equations can be converted into a first-order differential model. The sufficient conditions of the inertial neural network with neutral delay are derived by constructing suitable Lyapunov-Krasovskii functional candidates, introducing new free weighting matrices, utilizing inequality techniques and analytical method. Through the LMI condition, we analyze the global exponential stability of the delayed inertial neural networks in Lagrange sense. Meanwhile, the global exponential attractive set is also given. Finally, some example is given to illustrate our theoretical results.     

Global exponential stability for discrete-time neural networks with variable delays

This Letter provides new exponential stability criteria for discrete-time neural networks with variable delays. The main technique is to reduce exponential convergence estimation of the neural network solution to that of one component of the corresponding solution by constructing Lyapunov function based on M-matrix. By introducing the tuning parameter diagonal matrix, the delay-independent and delay-dependent exponential stability conditions have been unified in the same mathematical formula. The effectiveness of the new results are illustrated by three examples.