一类神经网络指数鲁棒稳定性分析

文中研究了一类变时滞区间神经网络的全局指数鲁棒稳定性。取消了变时滞参数为可导函数的假设,通过构造合适的Lyapunov函数,利用Halanay不等式和矩阵范数不等式,得到了一个新颖的区间神经网络全局指数鲁棒稳定的充分条件,该条件与系统的时滞参数无关。根据所得结论,还得到了一个线性矩阵不等式条件,该条件可以用LMI工具箱验证,便于在实际中的应用。最后通过一个数值例子和相应的计算机仿真结果验证了所得结果的有效性。     

参数不确定的单时滞系统基于简化的L-K泛函的稳定性分析

参数不确定和时滞广泛存在于各种实际的控制系统中,而且它们往往是导致系统不稳定或性能下降的原因。本文基于Lyapunov稳定性理论,通过构造简化的Lyapunov-Krasovskii泛函,同时应用线性矩阵不等式(LMI:linearmatrix inequality)方法,研究了参数不确定和单时变时滞系统的鲁棒稳定性问题,并导出了由LMI表示的该类系统的鲁棒稳定性判据,而且,通过这类简化的L-K泛函,在充分利用时滞信息的基础上减少了判据的保守性。最后借助含不确定性扰动的具有单时变时滞的单机-无穷大系统模型,分析了保持鲁棒稳定时系统可承受的最大时滞的界限,数值仿真验证了方法的有效性。     

时滞依赖型区间时滞系统非脆弱H_∞控制

针对一类状态和控制输入矩阵均为区间矩阵的不确定时滞系统,其中状态和控制输入同时具有未知但有上界的时间滞后,基于Lyapunov稳定性理论,利用线性矩阵不等式(LMI)方法,讨论了该类时滞系统的时滞依赖型非脆弱H∞状态反馈控制器设计问题.在区间不确定性和控制器执行机构扰动均满足增益有界条件下,得到了该类时滞系统的满足H∞性能的一个充分条件.通过求解一个线性矩阵不等式(LMIs)组,即可获得鲁棒H∞控制器.最后对某型飞机作机动飞行仿真,仿真结果表明该鲁棒控制器设计方法是有效的.     

多时滞Cohen-Grossberg神经网络鲁棒稳定性的新判据

分析了一类具有多时滞及参数摄动的Cohen-Grossberg神经网络的全局鲁棒稳定性.通过构造适当的Lyapunov泛函,以线性矩阵不等式形式给出了平衡点全局鲁棒稳定的判据.此外,所有结论的建立都不需要假定互连矩阵的对称性及激活函数的可微性和单调性.仿真结果进一步证明了结论的有效性.     

一类非线性不确定时滞系统的记忆与无记忆复合H∞状态反馈控制

针对一类具有状态非线性不确定性的线性时滞系统，基于Lyapunov稳定性理论，利用线性矩阵不等式（LMI）方法，讨论了该类时滞系统的记忆与无记忆复合H∞状态反馈控制器的设计问题。在非线性不确定性满足增益有界条件下，得到了该类时滞系统的满足鲁棒H∞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H∞控制器。     

区间矩阵的Hurwitz与Schur鲁棒稳定性检验

提出基于二维面检验的区间矩阵Ｈｕｒｗｉｔｚ与Ｓｃｈｕｒ鲁棒稳定的充分必要条件。证明区间矩阵的Ｈｕｒｗｉｔｚ与Ｓｃｈｕｒ鲁棒稳定性可由其二维表面的稳定性保证。为证明本文区间矩阵的鲁棒稳定性检验的可应用性，给出了实例。     

具有时滞和的非线性系统的鲁棒稳定性分析

针对具有时滞和及模有界参数不确定性的非线性系统,研究了鲁棒稳定性问题。通过构造新的Lyapunov泛函。其中考虑了时变时滞和时滞上界信息,并应用新的方法估计Lyapunov泛函导数的上界,以线性矩阵不等式形式给出了系统的时滞相关型稳定性判据。数值实例表明了结果的有效性和较小保守性。     

基于LMI的非线性模糊脉冲奇异摄动系统的鲁棒模糊控制

通过推广一般T-S模糊模型定义了一类非线性模糊脉冲奇异摄动系统,基于线性矩阵不等式(LMI)方法提出一种鲁棒模糊控制新方案,采用并行分布补偿(PDC)的基本思想设计状态反馈控制器,并利用Lyapunov理论证明闭环系统全局指数稳定.最后基于LMI方法,将鲁棒模糊控制器的设计问题转化为线性矩阵不等式问题(LMIP).仿真结果表明了该方法的有效性.     

一类线性不确定切换系统的非脆弱控制器设计

针对一类线性不确定切换系统,利用公共Lyapunov函数的方法,给出了当所设计的控制器存在加性摄动时鲁棒非脆弱控制器存在的条件。该控制器能够保证闭环切换系统在任意切换律下渐近稳定。然后应用线性矩阵不等式将鲁棒非脆弱控制器的设计问题转化为一组线性矩阵不等式的可行解问题,从而可借助Matlab中的LMI工具箱直接求解。最后通过仿真算例验证所提方法的有效性。     

考虑压电陶瓷不确定性的鲁棒自适应控制

选择信息熵作为判定相似性的工具,在判定数据相似性的基础上选择控制对象等效模型参数。采用简单的一阶惯性模型等效复杂的压电陶瓷模型。考虑实际压电器件的不确定性,在等效模型中,将不确定性视为符合高斯分布的变量。考虑不确定参数的影响,基于线性矩阵不等式(LMI)法的鲁棒镇定,保证系统的鲁棒稳定性。选定控制目标,使用自适应李雅普诺夫(Lyapunov)函数方法设计模型控制器。仿真结果验证控制策略效果良好。     

Fault Estimation for Nonlinear Dynamic Systems

In this paper, the problems of fault detection and estimation for nonlinear dynamic systems are considered by using fault detection observer and adaptive fault diagnosis observer. Based on Lyapunov stability theory and linear matrix inequality (LMI) techniques, a new sufficient condition in terms of LMIs for the proposed problem is derived. At the same time, we get the adaptive fault estimation algorithm. The LMI condition can be easily solved by MATLAB LMI toolbox. Finally, a flexible joint robotic example is given to illustrate the efficiency of the proposed approach.     

Parameter-Dependent Lyapunov Function Method for a Class of Uncertain Nonlinear Systems with Multiple Equilibria

First, a new linear matrix inequality (LMI) characterization of extended strict positive realness is presented for linear continuous-time systems. Then a class of nonlinear systems with multiple equilibria subject to polytopic uncertainty is addressed by the parameter-dependent Lyapunov function method. New sufficient conditions for global convergence are presented. This allows the Lyapunov function to be parameter dependent. Furthermore, an LMI-based controller design method is also given, and reduced-order controllers can be designed by performing a structural constraint on the introduced slack variables. Several numerical examples are included to demonstrate the applicability of the proposed method.     

一类非线性互联系统的H∞模型参考跟踪分散输出反馈模糊控制

本文对一类不确定状态不可测非线性互联系统,给出了一种基于观测器的H_∞模型参考跟踪分散输出反馈模糊控制方法.设计中,首先采用模糊不确定T-S模型对非线性互联系统进行模糊建模,在此基础上,给出模糊分散观测器的H_∞设计和基于观测器的模型参考跟踪分散模糊控制的设计.应用李亚普诺夫和线性矩阵不等式方法给出了模糊分散系统稳定的充分条件.仿真结果进一步验证了所提出的模糊分散控制方法的有效性.     

Adaptive Control with Guaranteed Contraction Rate for Systems with Actuator Saturation

The problem of adaptive control of linear discrete-time systems with actuator saturation and unknown parameters is investigated. A novel optimal control method is presented first for linear systems with known parameters and constant actuator saturation by introducing a Lyapunov function and a performance cost function that are both dependent on a contraction rate parameter. Based on the obtained guaranteed contraction-rate control method, an adaptive control algorithm is derived for systems containing unknown system parameters and time-varying actuator saturation. To show that the closed-loop system is stable and that the adaptive control algorithm is convergent, the Lyapunov function is supplemented by an additional part defined by the trace of a quadratic function of the controller gain. The effectiveness and potential of the presented method is demonstrated by a numerical example.     

Robust Constrained Model Predictive Control Based on Parameter-Dependent Lyapunov Functions

The problem of robust constrained model predictive control (MPC) of systems with polytopic uncertainties is considered in this paper. New sufficient conditions for the existence of parameter-dependent Lyapunov functions are proposed in terms of linear matrix inequalities (LMIs), which will reduce the conservativeness resulting from using a single Lyapunov function. At each sampling instant, the corresponding parameter-dependent Lyapunov function is an upper bound for a worst-case objective function, which can be minimized using the LMI convex optimization approach. Based on the solution of optimization at each sampling instant, the corresponding state feedback controller is designed, which can guarantee that the resulting closed-loop system is robustly asymptotically stable. In addition, the feedback controller will meet the specifications for systems with input or output constraints, for all admissible time-varying parameter uncertainties. Numerical examples are presented to demonstrate the effectiveness of the proposed techniques.     

Lyapunov Equation for the Stability of 2-D Systems

An analogue of the characterization of asymptotic stability of the 1-D systems by the solvability of associated Lyapunov equation is proposed here for 2-D systems. It is shown that internal stability of Roesser model is equivalent to the feasibility of some linear matrix inequality (LMI), related to quadratic Lyapunov functions.     

Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions

This paper investigates the problem of stability analysis and stabilization for two-dimensional (2-D) discrete fuzzy systems. The 2-D fuzzy system model is established based on the Fornasini–Marchesini local state-space model, and a control design procedure is proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, nonquadratic stability conditions are derived by means of linear matrix inequality (LMI) technique. Then, by introducing an additional instrumental matrix variable, the stabilization problem for 2-D fuzzy systems is addressed, with LMI conditions obtained for the existence of stabilizing controllers. Finally, the effectiveness and advantages of the proposed design methods based on basis-dependent Lyapunov functions are shown via two examples.     

Robust Dichotomy Analysis and Synthesis With Application to an Extended Chua's Circuit

Dichotomy, or monostability, is one of the most important properties of nonlinear dynamic systems. For a dichotomous system, the solution of the system is either unbounded or convergent to a certain equilibrium, thus periodic or chaotic states cannot exist in the system. In this paper, a new methodology for the analysis of dichotomy of a class of nonlinear systems is proposed, and a linear matrix inequality (LMI)-based criterion is derived. The results are then extended to uncertain systems with real convex polytopic uncertainties in the linear part, and the LMI representation for robust dichotomy allows the use of parameter-dependent Lyapunov function. Based on the results, a dynamic output feedback controller guaranteeing robust dichotomy is designed, and the controller parameters are explicitly expressed by a set of feasible solutions of corresponding linear matrix inequalities. An extended Chua's circuit with two nonlinear resistors is given at the end of the paper to demonstrate the validity and applicability of the proposed approach. It is shown that by investigating the convergence of the bounded oscillating solutions of the system, our results suggests a viable and effective way for chaos control in nonlinear circuits.