多组滞后非线性控制大系统的结构与关联鲁棒镇定

建立了一类多组多滞后区间时变非线性控制大系统的结构概念，采用李雅普诺夫函数鲁棒镇定等价法，给出了无滞后和扰动结构参数线性时变控制大系统的关联镇定，它蕴含了具有扰动结构参数的多组多滞后区间时变非线性关联控制大系统的结构与关联鲁棒镇定，同时给出了扰动参数与滞后非线性项界限的估计公式。     

时滞测度型时变脉冲大系统的全局指数稳定性

运用比较原理和导数不连续的李雅普诺夫函数，结合分解集结等方法，研究具有滞后的测度型线性时变脉冲扰动大系统的全局指数稳定性。结果表明，在一定条件下，由相应较低阶的定常时滞比较系统的指数稳定性，可得到时滞脉冲扰动时变大系统零解的全局指数稳定性。     

基于分散反馈控制的时滞混沌大系统

研究一类具有时滞关联的时滞大系统的混沌现象和分散反馈控制问题。应用线性矩阵不等式（LMI）方法,基于李雅普诺夫定理,分别得到了系统存在分散时滞反馈控制器和分散标准反馈控制器的充分条件,并利用分散时滞反馈控制器对系统中存在的不稳定周期轨道的追踪控制问题进行研究。仿真结果表明控制器具有很强的鲁棒性。     

一类参数不确定时滞系统的保成本控制

通过构造参数相关的李雅普诺夫函数,利用S-procedure方法研究一类具有参数不确定性和状态滞后的线性动态系统,得到了这类不确定时滞系统存在保成本控制器的充分条件.     

测度型脉冲时滞大系统的指数稳定性

本文借助加权范数型向量李雅普诺夫函数和积分型时滞比较原理，首次研究了测度型脉冲时滞线性时变大系统的指数稳定性。     

新型Lyapunov函数方法的模糊控制器设计

研究了在新型Lyapunov方法下的带有不确定性的T—S模糊模型稳定性及控制器的设计,给出了输入为零时系统稳定的充分条件,并验证了该条件比常用李雅普诺夫函数具有更大的松弛性。基于新型李雅普诺夫函数,对带有不确定性模糊模型设计了线性矩阵不等式形式的模糊控制器,该方法不必知道某一时刻被激活的规则数,同时把一个公共矩阵的寻找分解为p个矩阵的寻找。仿真实验证明,通过应用改进的李雅普诺夫函数设计的模糊控制器,具有良好的鲁棒性,控制效果良好。     

大型控制系数参数稳定域之扩大（2）

本文应用Riccati矩阵微分方程的对称正定解做出了二次型的李雅普诺夫函数,并应用向量李雅普诺夫函数法与比较原理,扩大了线性时变控制大系统的参数稳定域。     

具有有界控制输入的状态反馈控制系统闭环稳定性

本文基于李雅普诺夫定理,给出了具有有界控制输入的离散时间系统和连续时间控制系统的闭环渐近稳定性判据。利用不考虑控制约束时闭环系统李雅普诺夫矩阵方程解,得出了当控制输入有界时,线性状态反馈控制系统为渐近稳定的充分条件。这些判据具有简单的形式,并且易于计算。     

基于凸多面体方法的时滞和连续系统稳定性分析

针对一类状态向量中含有时滞和的连续系统,研究其时滞相关稳定性问题。利用凸组合方法和积分不等式并构造合适的李雅普诺夫泛函,以线性矩阵不等式形式给出了保证系统稳定的时滞相关充分条件,该线性矩阵不等式形式的系统稳定条件易于验证。由于在对李雅普诺夫泛函求导过程中使用了凸多面体方法,使得所得到的结论具有更小的保守性,仿真算例验证了结论的有效性。     

具有多滞后非线性定常关联控制系统的镇定性研究

建立了多组多滞后定常非线性控制系统的结构 概念,采用李雅普诺夫函数分解等价法,由 Riccati矩阵微分方程的对称正定解矩阵构造正 定二次型Ｖ函数,给出了无滞后无扰动参数线性定常控制孤立子系统的镇定性,蕴含具有滞 后控制向量函数的扰动结构参数的多组多滞后区间系数定常非线性关联控制系统的关联鲁棒 镇定的一个充分条件,同时给出了扰动参数与滞后非线性项界线的估计公式．     

具有区间时滞的不确定性随机时滞系统的时滞相关鲁棒稳定性

针对具有区间时滞的不确定性随机时滞系统, 进行稳定性分析. 通过考虑变时滞、时滞的上界及它们的差三者之间的关系, 并应用公式和Lyapunov稳定性理论, 在不忽略任何有用项的前提下, 得到改进的具有区间时滞的随机系统的稳定性判据. 数值实例验证了该方法的有效性.     

Exponential stability of switched stochastic delay systems with non-linear uncertainties

This article considers the robust exponential stability of uncertain switched stochastic systems with time-delay. Both almost sure (sample) stability and stability in mean square are investigated. Based on Lyapunov functional methods and linear matrix inequality techniques, new criteria for exponential robust stability of switched stochastic delay systems with non-linear uncertainties are derived in terms of linear matrix inequalities and average dwell-time conditions. Numerical examples are also given to illustrate the results.     

Robust exponential stability of uncertain stochastic systems with probabilistic time‐varying delays

This paper is concerned with the problem of delay‐distribution–dependent robust exponential stability for uncertain stochastic systems with probabilistic time‐varying delays. Firstly, inspired by a class of networked systems with quantization and packet losses, we study the stabilization problem for a class of network‐based uncertain stochastic systems with probabilistic time‐varying delays. Secondly, an equivalent model of the resulting closed‐loop network‐based uncertain stochastic system is constructed. Different from the previous works, the proposed equivalent system model enables the controller design of the network‐based uncertain stochastic systems to enjoy the advantage of probability distribution characteristic of packet losses. Thirdly, by applying the Lyapunov‐Krasovskii functional approach and the stochastic stability theory, delay‐distribution–dependent robust exponential mean‐square stability criteria are derived, and the sufficient conditions for the design of the delay‐distribution–dependent controller are then proposed to guarantee the stability of the resulting system. Finally, a case study is given to show the effectiveness of the results derived. Moreover, the allowable upper bound of consecutive packet losses will be larger in the case that the probability distribution characteristic of packet losses is taken into consideration.     

Delay-segment-dependent robust stability for uncertain discrete stochastic Markovian jumping systems with interval time delay

This article deals with the problem of robust stochastic stability for a class of uncertain discrete stochastic Markovian jumping systems with time-varying interval delay. By constructing a parameter-dependent Lyapunov–Krasovskii functional and checking its difference in two subintervals, respectively, some novel delay-segment-dependent stability criteria for the addressed system are derived. Two simulation examples are given to show effectiveness of the proposed method.     

Robust sampled‐data control for Itô stochastic Markovian jump systems with state delay

In this paper, the problem of robust sampled‐data control for Itô stochastic Markovian jump systems (Itô SMJSs) with state delay is investigated. Using parameters‐dependent Lyapunov functionals and some stochastic equations, we give stochastic sufficient stability criteria for polytopic uncertain Itô SMJSs. As a corollary, stochastic sufficient stability criteria are given for nominal Itô SMJSs. For this two cases of Itô SMJSs, based on the obtained stochastic stability criteria, their time‐independent sampled‐data controllers are designed, respectively. Then, for designing a time‐dependent sampled‐data controller for Itô SMJSs, a parameters‐dependent time‐scheduled Lyapunov functional is developed. New stochastic sufficient stability criteria are obtained for polytopic uncertain Itô SMJSs and nominal Itô SMJSs. Furthermore, their time‐dependent sampled‐data controllers are designed, respectively. Lastly, a numerical example is provided to illustrate the effectiveness of the proposed method.     

Robustly Exponential Stability Analysis for Discrete-Time Stochastic Neural Networks with Interval Time-Varying Delays

This paper deals with the problems of the global exponential stability and stabilization for a class of uncertain discrete-time stochastic neural networks with interval time-varying delay. By using the linear matrix inequality method and the free-weighting matrix technique, we construct a new Lyapunov–Krasovskii functional and establish new sufficient conditions to guarantee that the uncertain discrete-time stochastic neural networks with interval time-varying delay are globally exponential stable in the mean square. Furthermore, we extend our consideration to the stabilization problem for a class of discrete-time stochastic neural networks. Based on the state feedback control law, some novel delay-dependent criteria of the robust exponential stabilization for a class of discrete-time stochastic neural networks with interval time-varying delay are established. The controller gains are designed to ensure the global robust exponential stability of the closed-loop systems. Finally, numerical examples illustrate the effectiveness of the theoretical results we have obtained.     

Robust stochastic stability of uncertain discrete-time impulsive Markovian jump delay systems with multiplicative noises

In this paper, the robust stochastic stability is investigated for a class of uncertain discrete-time impulsive Markovian jump delay systems with multiplicative noises. Using the method of stochastic Lyapunov functionals construction, it is shown that impulses can stabilise the original impulse-free unstable systems. Moreover, the stability property of the impulse-free systems can be retained in the cases of appropriately large impulsive time interval. Some numerical examples are exploited to demonstrate the effectiveness and the superiority of the proposed results.     

具有无穷时滞的不确定大系统的鲁棒镇定

研究了具有无穷时滞的不确定微分－积分大系统的鲁棒稳定性问题，对每个子系统的应用稳定的局部状态反馈，利用Lyapunov函数法并结合不等式分析技巧，给出了具有无穷时滞的不确定微分－积分大系统的鲁棒全局一致近稳定的充分条件。     

具有时滞的不确定鲁里叶控制系统的绝对鲁棒稳定性

讨论了具有时滞的非线性不确定鲁里叶控制系统的鲁棒绝对稳定性问题,应用Bellman-Gronwell不等式和Lyapunov泛函方法研究了不确定鲁里叶控制系统的鲁棒绝对稳定性并给出了系统的滞相关稳定和时滞无关稳定的充分判据,运用这些条件可以直接估计具有时滞的非线性不确定鲁里叶控制系统的鲁棒绝对稳定界和时滞界。     

Robust stabilization of stochastic systems based on the LQ controller

The robust exponential stability in mean square for a class of linear stochastic uncertain control systems is dealt with. For the uncertain stochastic systems, we have designed an optimal controller which guarantees the exponential stability of the system. Actually, we employed Lyapunov fimction approach and the stochastic algebraic Riccati equation (SARE) to have shown the robusmess of the linear quadratic(LQ) optimal control law.And the algebraic criteria for the exponential stability on the linear stochastic uncertain closed-loop systems are given.