非线性滞后Ito随机系统的滞后无关均方渐近稳定性

研究非线性滞后Ｉｔｏ随机系统的滞后无关均方渐近稳定性，将关于线性时滞不等式的Ｈａｌａｎａｙ不等式推广到非线性情形，用Ｌｙａｐｕｎｏｖ函数和关于时滞随机系统的比较原理，得到了非线性滞后Ｉｔｏ随机系统滞后无关均方渐近稳定性的一些判据。     

一类随机非线性系统的有限时间H∞控制

本文研究一类随机非线性系统的有限时间H_∞控制问题.考虑闭环系统在有限时间间隔内的瞬态性能和抗干扰能力,对伊藤型随机非线性系统进行了研究.利用Lyapunov函数和线性矩阵不等式(LMI)得到了系统满足均方有限时间有界的充分条件,进一步设计了有限时间H_∞控制器,并给出了系统满足均方有限时间有界和相应H_∞性能的充分条件.最后给出了两个例子验证了该方法的有效性和可行性.     

非线性不确定中立型系统的鲁棒H∞控制

考虑系统外界干扰、系统参数摄动等非线性扰动环节对中立型时滞系统的H∞影响,提出基于Lyapunov稳定性理论的鲁棒H∞控制器的设计思想.利用线性矩阵不等式(LMI)方法,给出了该类具有状态非线性不确定性中立型时滞系统的鲁棒∞控制器的设计实例.在非线性不确定函数满足增益有界的条件下,得到了该类时滞系统满足鲁棒∞性能的一个充分条件.通过求解一个线性矩阵不等式LMI,即可获得鲁棒∞控制器.仿真结果表明了基于Lyapunov稳定性理论,LMI技术设计的控制器克服了系统外界非线性干扰或系统本身非线性参数摄动的影响,实现了闭环系统的H∞性能条件下的渐近稳定,满足了该系统鲁棒H∞控制的要求.     

网络攻击下电力系统的离散迟滞量化控制

针对随机网络系统受到攻击时的稳定问题，设计了一种基于离散时间观测状态和模态的迟滞量化反馈控制器，使得闭环随机系统均方指数稳定。离散观测减少了控制器接收到的信号并且保证信号主要内容不失真，从而提高控制器的效率，降低了网络通信负担。采用迟滞量化器有效地避免了对数量化器在量化过程中产生的抖震现象，并且考虑了当网络系统遭到网络欺骗攻击时，控制器能否保证系统的稳定性问题。给出均方指数稳定下的判据条件，根据稳定性判据条件设计基于离散状态和模态观测的迟滞量化反馈控制器，利用Lyapunov理论证明了随机网络非线性系统的均方指数稳定性，检验了判据条件的有效性。通过数值仿真验证了理论结果的有效性。     

线性不确定中立型时滞系统的鲁棒二次性能

研究具有非匹配条件的范数有界线性不确定中立型时滞系统的稳定和二次性能控制问题．基于Lyapunov方法，提出了系统鲁棒渐近稳定并满足给定二次性能指标的时滞相关型条件，该条件等价干线性矩阵不等式(LMI)可解性问题，并根据LMI的可行解，构造了状态反馈控制器设计方法．     

非线性M IMO 系统H 2 öH ∞模糊输出反馈控制

研究了非线性MIMO系统H2／H∞模糊输出反馈控制问题．采用局部线性化方法，用T—S模糊线性模型逼近非线性系统．在希望的H∞干扰抑制约束下，通过最小化H2控制性能指标，实现了模糊输出反馈次优控制．通过将优化问题转化成特征值问题(EVP)，应用线性矩阵不等式(LMI)优化方法求解，简化了问题的求解过程．所设计的闭环系统在平衡点是局部二次型稳定的，系统抗扰性能和动态性能均较好．     

一类非线性时滞广义系统的状态反馈控制

利用线性矩阵不等式(LMI),讨论了一类非线性时滞广义系统的状态反馈控制问题.通过对非线性映射Frechet导数的逆矩阵的估计,给出了系统渐近稳定的充分条件.这一条件与时滞相关,可归结为一个线性矩阵不等式的可解性.在LMI有解的条件下,可得到系统状态反馈控制器的参数表示.数值实例表明该方法是有效的.     

一类不确定的2D 非线性时滞系统的鲁棒能稳

研究一类参数不确定的2D时滞系统满足Lipschitz条件的非线性Fornasini Marchesini 模型（简称2 DFM II）的鲁棒能稳问题,即设计静态状态反馈控制律，使得对所有容许的不确定参数，闭环系统稳定．通过求解线性矩阵不等式（LMI），给出了问题可解的充分条件及静态状态反馈控制律的设计方法．最后通过数值算例验证了方法的有效性．     

基于H∞滤波器的非线性摄动时滞系统的故障诊断

针对一类非线性摄动时滞系统，基于H∞滤波器技术，探讨了系统的故障诊断问题．首先引入参考模型，通过构建故障观测器，形成能反映系统故障的广义残差模型；然后通过基于线性矩阵不等式（LMI）的方法，将故障诊断问题转化为系统鲁棒稳定性分析问题，并给出该问题解存在的LMI条件和求法．该方法既提高了故障观测器对残差的敏感性，又有效地抑制了干扰，提高了故障检测的效果．仿真结果表明了该算法的有效性．     

具有滞后耦合特性的线性随机大系统的时滞无关均方稳定性*

本文研究具有滞后耦合特性的时不变线性Ｉｔｏ随机大系统的稳定性，得到了大系统平衡态滞后无关的均方渐近稳定性代数判据．文中所考虑的子系统是随机子系统，对它们的假设正好是它们均方渐近稳定的充要条件．另外，文中采用的Ｌｙａｐｕｎｏｖ泛函是确定型的Ｌｙａｐｕｎｏｖ泛函．     

Lyapunov-based adaptive state estimation for a class of nonlinear stochastic systems

This paper is concerned with an adaptive state estimation problem for a class of nonlinear stochastic systems with unknown constant parameters. These nonlinear systems have a linear-in-parameter structure, and the nonlinearity is assumed to be bounded in a Lipschitz-like manner. Using stochastic counterparts of Lyapunov stability theory, we present adaptive state and parameter estimators with ultimately exponentially bounded estimator errors in the sense of mean square for both continuous-time and discrete-time nonlinear stochastic systems. Sufficient conditions are given in terms of the solvability of LMIs. Moreover, we also introduce a suboptimal design approach to optimizing the upper bound of the mean-square error of parameter estimation. This suboptimal design procedure is also realized by LMI computations. By a martingale method, we also show that the related Lyapunov function has a non-negative Lyapunov exponent.     

Delay-dependent stabilization of stochastic interval delay systems with nonlinear disturbances

In this paper, a delay-dependent approach is developed to deal with the robust stabilization problem for a class of stochastic time-delay interval systems with nonlinear disturbances. The system matrices are assumed to be uncertain within given intervals, the time delays appear in both the system states and the nonlinear disturbances, and the stochastic perturbation is in the form of a Brownian motion. The purpose of the addressed stochastic stabilization problem is to design a memoryless state feedback controller such that, for all admissible interval uncertainties and nonlinear disturbances, the closed-loop system is asymptotically stable in the mean square, where the stability criteria are dependent on the length of the time delay and therefore less conservative. By using Itô's differential formula and the Lyapunov stability theory, sufficient conditions are first derived for ensuring the stability of the stochastic interval delay systems. Then, the controller gain is characterized in terms of the solution to a delay-dependent linear matrix inequality (LMI), which can be easily solved by using available software packages. A numerical example is exploited to demonstrate the effectiveness of the proposed design procedure.     

A note on the robust stability of uncertain stochastic fuzzy systems with time-delays

Takagi-Sugeno (T-S) fuzzy models are now often used to describe complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning applied to a set of linear submodels. In this note, the T-S fuzzy model approach is exploited to establish stability criteria for a class of nonlinear stochastic systems with time delay. Sufficient conditions are derived in the format of linear matrix inequalities (LMIs), such that for all admissible parameter uncertainties, the overall fuzzy system is stochastically exponentially stable in the mean square, independent of the time delay. Therefore, with the numerically attractive Matlab LMI toolbox, the robust stability of the uncertain stochastic fuzzy systems with time delays can be easily checked.     

A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances

This paper is concerned with the state feedback control problem for a class of discrete-time stochastic systems involving sector nonlinearities and mixed time-delays. The mixed time-delays comprise both discrete and distributed delays, and the sector nonlinearities appear in the system states and all delayed states. The distributed time-delays in the discrete-time domain are first defined and then a special matrix inequality is developed to handle the distributed time-delays within an algebraic framework. An effective linear matrix inequality (LMI) approach is proposed to design the state feedback controllers such that, for all admissible nonlinearities and time-delays, the overall closed-loop system is asymptotically stable in the mean square sense. Sufficient conditions are established for the nonlinear stochastic time-delay systems to be asymptotically stable in the mean square sense, and then the explicit expression of the desired controller gains is derived. A numerical example is provided to show the usefulness and effectiveness of the proposed design method.     

New observer‐based controller design for LPV stochastic systems with multiplicative noise

This paper addresses an observer‐based control problem of Linear Parameter Varying (LPV) stochastic systems. Based on the modeling approaches, the LPV stochastic systems can be represented by a set of linear systems with multiplicative noise term. To solve the observer‐based control problem, a less conservative stability criterion is developed via the chosen Parameter‐Dependent Lyapunov Function (PDLF). In the PDLF, none element in the positive definite matrix is required as zero. Besides, an Extended Projection Lemma is proposed to convert the derived sufficient conditions into Linear Matrix Inequality (LMI) form. According to the derived LMI conditions, all feasible solutions can be found by convex optimization algorithm at a single step. Based on those feasible solutions, an observer‐based Gain‐Scheduled (GS) controller can be established to guarantee the asymptotical stability of the closed‐loop system in the sense of mean square. Finally, two numerical examples are provided to demonstrate the effectiveness and applicability of the proposed method.     

Stability analysis and stabilization control of multi-variable switched stochastic systems

In this paper, the mean square (MS) stability and exponential mean square (EMS) stability of multi-variable switched stochastic systems are investigated. Based on the concept of the average dwell-time and the ratio of the total time running on all unstable subsystems to the total time running on all stable subsystems, some sufficient conditions are given to ensure the MS stability and EMS stability of the switched stochastic systems involved. Further, for the switched stochastic control systems with all subsystems controllable or stabilizable, EMS stabilization controls and sufficient conditions on EMS stabilization are presented, and the convergent rates of the closed-loop systems are obtained.     

Mean square exponential stability in high-order stochastic impulsive BAM neural networks with time-varying delays

In this paper, a class of stochastic impulsive high-order BAM neural networks with time-varying delays is considered. By using Lyapunov functional method, LMI method and mathematics induction, some sufficient conditions are derived for the globally exponential stability of the equilibrium point of the neural networks in mean square. It is believed that these results are significant and useful for the design and applications of impulsive stochastic high-order BAM neural networks.     

H ∞ filtering for discrete-time singular networked systems with communication delays and data missing

In this article, the problem of H _∞ filter design is investigated for discrete-time singular networked systems with both multiple stochastic time-varying communication delays and probabilistic missing measurements. Two kinds of stochastic time-varying communication delays, namely stochastic discrete delays and stochastic distributed delays, are simultaneously considered. The purpose of the addressed filtering problem is to design a filter such that, for the admissible random measurement missing and communication delays, the filtering error dynamics is asymptotically stable in the mean square with a prescribed H _∞ performance index. In terms of linear matrix inequality (LMI) method, a sufficient condition is established that ensures the asymptotical stability in the mean square with a prescribed H _∞ performance index of the filtering error dynamics and then the filter parameters are characterised by the solution to an LMI. A numerical example is introduced to demonstrate the effectiveness of the proposed design procedures.     

State-feedback ℋ∞ control for stochastic time-delay nonlinear systems with state and disturbance-dependent noise

This article focuses on the state-feedback ?_∞ control problem for the stochastic nonlinear systems with state and disturbance-dependent noise and time-varying state delays. Based on the maxmin optimisation approach, both the delay-independent and the delay-dependent Hamilton–Jacobi-inequalities (HJIs) are developed for synthesising the state-feedback ?_∞ controller for a general type of stochastic nonlinear systems. It is shown that the resulting control system achieves stochastic stability in probability and the prescribed disturbance attenuation level. For a class of stochastic affine nonlinear systems, the delay-independent as well as delay-dependent matrix-valued inequalities are proposed; the resulting control system satisfies global asymptotic stability in the mean-square sense and the required disturbance attenuation level. By modelling the nonlinearities as uncertainties in corresponding stochastic time-delay systems, the sufficient conditions in terms of a linear matrix inequality (LMI) and a bilinear matrix inequality (BMI) are derived to facilitate the design of the state-feedback ?_∞ controller. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.     

非线性随机时滞系统的稳定性与应用

首先考虑了不确定性的一族非线笥随机时滞系统,建立了这种系统的均方指数稳定与几乎必须指数稳定的充分准则,其准则是时滞无关的,然后应用这些充分条件到一类不确定的随机时滞神经网络,得到了这咱神经网络指数稳定的产用判据。本文的结果是最近文献中某些结果的推广,最后一个数值例子说明的所给准则的有效性。