Delay-dependent robust stability of uncertain networked control systems with multiple state time-delays

In this paper, delay-dependent robust stability for a class of uncertain networked control systems （NCSs） with multiple state time-delays is investigated. Modeling of multi-input and multi-output （MIMO） NCSs with networkinduced delays and uncertainties through new methods are proposed. Some new stability criteria in terms of LMIs are derived by using Lyapunov stability theory combined with linear matrix inequalities （LMIs） techniques. We analyze the delay-dependent asymptotic stability and obtain maximum allowable delay bound （MADB） for the NCSs with the proposed methods. Compared with the reported results, the proposed results obtain a much less conservative MADB which are more general. Numerical example and simulation is used to illustrate the effectiveness of the proposed methods.     

Delay-dependent robust stability of uncertain fuzzy large-scale systems with time-varying delays

This paper addresses the stability problem of fuzzy large-scale systems (FLSSs) with uncertainties and arbitrary time-varying delays. The stability conditions, which are less conservative and more applicable than the existing results, are derived by a novel Lyapunov-Krasovskii functional method and expressed in terms of linear matrix inequalities (LMIs). Two examples are given to demonstrate the correctness and advantage of our theoretical results.     

时滞不确定采样控制系统的鲁棒稳定性

本文给出了一种可定量分析采样控制系统的时滞鲁棒稳定性的方法.因为采样系统的对象是连续时间的,所以对象中的时滞也应该是按连续时间来处理.文中指出,一个整数倍时滞是稳定的采样系统,可能会因为有并不很大的连续时间时滞而失稳.定义了一个新的变量w(t),用来描述这个不确定连续时间时滞带来的动特性.将w(t)的反馈回路分成与时滞无关和有关的两个部分,并提出了一种用频率响应来确定是否存在由不确定时滞引起的周期解的方法.用修正z-变换法和仿真验证了这个由图解解析所求得的解.本方法既可用于采样系统,也可用于一般的连续时间系统.     

Analysis of robust stability for switched systems with multiple time-delays

The sufficient conditions of delay-dependent exponential stability for switched systems and robust exponential stability for uncertain switched systems with two time-delays are presented by using average dwell time method and free-weighting matrix method.The interaction between different time-delays is considered.The sufficient conditions do not need that every subsystem is stable.The designed methods of the switching law are also given.The sufficient conditions are given in the form of linear matrix inequalities that can be solved easily.The result is proven to be valid by the simulation at last.     

多时滞Lurie控制系统的时滞相关鲁棒稳定性

时滞Lurie控制系统的稳定性条件与Lyapunov函数的选取有关.本文对多时滞Lurie控制系统进行了变换,然后选择一个适当的Lyapunov函数,利用Lyapunov稳定性方法并结合Moon引理,得到了多时滞Lurie控制系统的时滞相关鲁棒稳定性判别条件,该条件是以线性矩阵不等式(LMI)给出的,可用Matlab求解.最后用一个算例验证了所得方法的有效性.     

多时滞不确定网络控制系统的时滞独立稳定判据

针对一类多输入多输出（MIMO）网络控制系统．在考虑多重分布时滞和不确定性的情况下．建立了该系统的连续时闻数学模型．利用Lyapunov稳定性理论,结合线性矩阵不等式（LMI）方法和S-过程,给出了基于LMI形式的时滞独立渐近稳定判据．通过这些判据,能分析和判定具有多重时滞和不确定性的网络控制系统的时滞独立渐近稳定性．与已有的方法相比,该方法更加有效且求解方便．数值仿真结果表明了该方法的有效性．     

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.     

Less conservative robust stability criteria for uncertain discrete stochastic singular systems with time-varying delay

The problem of robust stabilisation for uncertain discrete singular systems with time-varying delay is discussed in this article. First, a new delay-distribution-dependent Lyapunov function is established. Then, sufficient conditions are proposed for guaranteeing that the uncertain discrete singular system with time-varying delay has the properties of regularity, causality and stability. Finally, a suitable robust state feedback controller is designed by linear matrix inequality. Numerical examples illustrate that the results derived from the proposed method are less conservative than the existing ones.     

New results on delay-dependent robust stability criteria of uncertain fuzzy systems with state and input delays

This paper focuses on the delay-dependent stability analysis and stabilization for uncertain T-S fuzzy control systems with state and input delays. The key features of the approach include the introduction of uncorrelated augmented matrix items into the Lyapunov functional and the use of a tighter bounding technology. In fact, these techniques lead to more general and less conservative stability conditions that guarantee a wide stability region. Our delay-dependent stability conditions thus obtained are given in terms of linear matrix inequalities (LMIs). Finally, some examples are included to show that the proposed criteria improve the existing results significantly.     

基于观测器的不确定T-S模糊系统鲁棒镇定

为带有参数不确定性的T-S模糊控制系统提出了新的基于观测器的鲁棒输出镇定条件. 该条件用来设计模糊控制器和模糊观测器. 为了设计模糊控制器和模糊观测器, 用T-S模糊模型来表示非线性系统, 并运用平行分布补偿观念. 充分条件基于二次Lyapunov函数, 通过将模糊系统的鲁棒镇定条件表述为一系列矩阵不等式, 比以往文献中列出的条件具有更小的保守性. 该不等式为双线性矩阵不等式, 可分两步骤先后解得使T-S模糊系统镇定的控制器增益和观测器增益. 最后, 通过对一个具有不确定性的连续时间非线性系统控制的例子证明了提出方法比以往方法更宽松.     

Delay-independent robust stability of uncertain linear systems

In this paper we present some new sufficient conditions for robust stability of linear systems with uncertain time delay as well as structured parameter uncertainty. The stability robustness bounds obtained from the new sufficient conditions are independent of the size of time delay. Some illustrative examples are given.     

Further results on the robust stability of uncertain time-delay systems

We present new several sufficient conditions for the robust stability of uncertain time-delay systems. These conditions represent the delay-independent asymptotic stability and the decaying rate for uncertain single time-delay systems. These results are then extended to uncertain composite linear systems with time delays. The superiority of these results is demonstrated by comparing them to those given by Wang et al. (1987).     

Finite-time robust stochastic stability of uncertain stochastic delayed reaction-diffusion genetic regulatory networks

This paper is concerned with the problem of finite-time stability analysis for uncertain stochastic delayed reaction-diffusion genetic regulatory networks. The parameter uncertainties are assumed to be norm-bounded, and the time delays are assumed to be time-varying. Based on the Lyapunov functional method, sufficient conditions ensuring the networks to be finite-time robustly stochastically stable are established. When there are no norm-bounded parameter uncertainties in the networks, a finite-time stochastic stability condition is also established. All the conditions are diffusion-dependent as well as delay-dependent. Numerical examples are given to illustrate the effectiveness of the proposed results.     

不确定时滞系统的鲁棒绝对稳定性研究

基于Lyapunov稳定性理论，采用线性矩阵不等式处理方法，研究具有参数不确定性的时滞系统鲁棒绝对稳定性问题．导出了用线性矩阵不等式系统可行性描述的系统鲁棒绝对稳定的滞后依赖型条件，据此可计算出最大的允许时滞界．通过求解一组线性矩阵不等式，给出使得闭环系统鲁棒绝对稳定的无记忆状态反馈控制律设计方法。     

A note on robust stability bounds

The authors comment on stability robustness bounds for linear systems with multiple uncertain parameters which were obtained by means of Lyapunov functions. Results obtained with quadratic and with vector Lyapunov functions are compared. Simple examples are used to illustrate the effects of the choice of functions, corresponding majorizations, and system decompositions     

Stable and robust fuzzy control for uncertain nonlinear systems

Presents the stability and robustness analysis for multivariable fuzzy control systems subject to parameter uncertainties based on a single-grid-point (SGP) approach. To perform the analysis, we represent a multivariable nonlinear system using a TS-fuzzy plant model. Three design approaches of fuzzy controllers are introduced to close the feedback loop. By estimating the matrix measures of the system parameters and parameter uncertainties, stability and robustness conditions for different cases are derived. Application examples are given to show the design procedures and the merits of the proposed fuzzy controller     

T-S模糊时滞系统的时滞相关鲁棒稳定新判据

研究了基于Takagi-Sugeno（T-S）模糊模型描述的非线性时滞系统的稳定性和H∞扰动抑制问题,利用线性矩阵不等式（LMI）技术,导出了一种满足优化H∞性能的时滞相关稳定新判据,该判据不仅适用于系统时滞变化率大于1的情形,且与现有方法相比具有更小的保守性,数值仿真结果证明了所提方法的有效性。     

一类离散非线性不确定互联系统的模糊分散控制

利用模糊控制方法研究一类离散非线性互联系统的分散控制问题.首先采用模糊(T-S)模型对离散非线性不确定互联系统进行模糊建模,应用并行分布补偿算法(PDC)给出状态反馈分散模糊控制方案,并基于李亚普诺夫函数方法证明了闭环系统的稳定性.然后当系统的状态不完全可测时,设计模糊分散观测器来估计各子系统的状态,从而给出基于观测器的状态反馈分散模糊控制设计的方法.因为该分散模糊控制设计问题是以线性矩阵不等式的形式给出,所以很容易用凸优化方法求解.仿真结果验证了所提出控制方法的有效性.     

基于观测器的不确定非线性系统的自适应鲁棒模糊控制

针对单输入单输出不确定非线性系统提出了一种自适应鲁棒模糊控制算法.该算法通过设计观测器来估计系统的状态向量,因此不要求假设系统的状态向量是可测的.在这个算法中,主要的假设为最优逼近参数向量与标称参数向量之差的范数和逼近误差的界限是未知的.通过只对未知界限估计的调节,该算法减轻了在线计算量并且提高了系统的鲁棒性.所设计的自适应鲁棒模糊控制算法保证了闭环系统的所有信号是一致有界的并且跟踪误差估计收敛到一个小的零邻域内.仿真例子证实了所提方法的可行性.