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1.
Flávio A. Faria Geraldo N. Silva Vilma A. Oliveira 《International journal of systems science》2013,44(10):1956-1969
In this article, the fuzzy Lyapunov function approach is considered for stabilising continuous-time Takagi-Sugeno fuzzy systems. Previous linear matrix inequality (LMI) stability conditions are relaxed by exploring further the properties of the time derivatives of premise membership functions and by introducing slack LMI variables into the problem formulation. The relaxation conditions given can also be used with a class of fuzzy Lyapunov functions which also depends on the membership function first-order time-derivative. The stability results are thus extended to systems with large number of rules under membership function order relations and used to design parallel-distributed compensation (PDC) fuzzy controllers which are also solved in terms of LMIs. Numerical examples illustrate the efficiency of the new stabilising conditions presented. 相似文献
2.
《Fuzzy Systems, IEEE Transactions on》2006,14(5):640-653
We propose a new approach for the stability analysis of discrete Sugeno Types II and III fuzzy systems. The approach does not require the existence of a common Lyapunov function. We introduce the concept of fuzzy positive definite and fuzzy negative definite functions. This new concept is used to replace classical positive and negative definite functions in arguments similar to those of traditional Lyapunov stability theory. We obtain the equivalent fuzzy system for a cascade of two Type II/III fuzzy systems. We use the cascade of a system and a fuzzy Lyapunov function candidate to derive new conditions for stability and asymptotic stability for discrete Type II and Type III fuzzy systems. To demonstrate the new approach, we apply it to numerical examples where no common Lyapunov function exists. 相似文献
3.
一类T-S模糊控制系统的稳定性分析及设计 总被引:1,自引:0,他引:1
研究了一类输入采用双交叠模糊分划的T-S模糊控制系统稳定性分析及控制器设计问题.基于分段模糊Lyapunov函数,提出了一个新的判定开环T-S模糊系统稳定性的充分条件,该方法只需在各个模糊区间里满足模糊Lyapunov方法中的条件,其保守性比公共Lyapunov函数法和分段Lyapunov函数法的保守性更低.运用并行分布补偿法(PDC)进一步探讨了闭环T-S模糊控制系统的稳定性分析问题并设计了模糊控制器.最后,一个仿真示例说明了本文方法的有效性. 相似文献
4.
NON‐PDC Observer‐Based T‐S Fuzzy Tracking Controller Design and its Application in CHAOS Control
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In many mechanical devices with chaotic behavior, stabilizing unstable periodic orbits (UPOs) of the system has positive effects in the lifetime and effectiveness of these devices. In this study, a new non‐parallel distributed compensation (non‐PDC) observer‐based tracking controller is presented for Takagi–Sugeno fuzzy systems to control the chaotic behavior of such systems. Asymptotic stability synthesis of the closed‐loop system is investigated using a fuzzy Lyapunov function to derive less conservative conditions than common quadratic Lyapunov function‐based approaches. To tackle the main drawback of the fuzzy Lyapunov‐based approaches, which assume some upper bounds on the derivatives of the fuzzy grade functions, we propose a new procedure by considering a constraint on the control signal. The new design conditions are given in the form of linear matrix inequalities (LMIs). The proposed control structure is applied to spinning disks in which chaos phenomena appear in lateral vibration. Simulation results are given to show the applicability of the proposed tracker to the UPO problem. 相似文献
5.
The purpose of this paper is to investigate the stability of nonlinear systems represented by a Takagi‐Sugeno discrete‐time fuzzy model. The homogeneous polynomial matrix function (HPMF) is developed to obtain new stabilization conditions. Applying the HPMF to the non‐parallel distributed compensation (non‐PDC) law and non‐quadratic Lyapunov function, some new stabilization conditions are obtained by the following two means: (a) utilizing the popular idea of introducing additional variables for some fixed degree of the HPMF; and (b) increasing the degree of the HPMF. It is shown that the conditions obtained with approach (a) are less conservative than some sufficient stability conditions available in the literature to date. It is also shown that as the degree of HPMF increases the conditions obtained under (b) become less conservative. An example is provided to illustrate how the proposed approaches compare with other techniques available in the literature. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society 相似文献
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一类切换模糊时滞系统的状态反馈控制 总被引:2,自引:0,他引:2
针对切换模糊时滞系统,根据平行分布补偿算法,设计了模糊状态反馈控制器.使用切换技术及单Lyapunov函数和多Lyapunov函数方法,给出了这一类切换模糊时滞系统渐近稳定的充分条件及切换律.仿真结果表明了方法的有效性. 相似文献
8.
《Fuzzy Systems, IEEE Transactions on》2009,17(3):544-555
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10.
Qunxian Zheng Hongbin Zhang Dianhao Zheng 《International Journal of Control, Automation and Systems》2017,15(3):986-994
The stability analysis and asynchronous stabilization problems for a class of discrete-time switched nonlinear systems with stable and unstable subsystems are investigated in this paper. The Takagi-Sugeno (T-S) fuzzy model is used to represent each nonlinear subsystem. Through using the T-S fuzzy model, the studied systems are modeled into the switched T-S fuzzy systems. By using the switching fuzzy-basis-dependent Lyapunov functions (FLFs) approach and mode-dependent average dwell time (MDADT) technique, the stability conditions for the open-loop switched T-S fuzzy systems with unstable subsystems and asynchronous stabilization conditions for the closed-loop switched T-S fuzzy systems with unstable subsystems are obtained. Both the stability results and asynchronous stabilization results are derived in terms of linear matrix inequalities (LMIs). Finally two numerical examples are provided to illustrate the effectiveness of the results obtained. 相似文献
11.
More Relaxed Non‐Quadratic Stabilization Conditions Using Ts Open Loop System and Control Law Properties
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This paper proposes more relaxed stabilization conditions based on a non‐quadratic Lyapunov function (NQLF) and parallel distributed compensator (PDC) controller. The conditions are derived in terms of linear matrix inequalities (LMIs) by introducing three slack matrices based on the properties of TS membership functions, an open loop system and a PDC controller. These slack matrices are utilized to decouple the LMI variables from the TS system and the input matrices. Therefore, the proposed approach greatly reduces the number of LMI conditions and improves feasibility by providing more degrees of freedom compared to recently published studies. Moreover, local stability and stabilization conditions are considered to handle the time derivatives of membership functions appearing in the stabilization synthesis of the TS closed‐loop system with PDC controller. Finally, several examples are presented to demonstrate the advantages of the proposed approaches. 相似文献
12.
针对一类 Takagi-Sugeno (T-S) 连续模糊系统, 在分析模糊系统前提规则结构信息的基础上, 研究了其稳定性和保性能设计问题. 通过将模糊 Lyapunov 函数 (FLF) 和分段二次 Lyapunov 函数 (PQLF) 结合, 构造出分段模糊 Lyapunov 函数 (PFLF), 并提出了一种新的并行分配补偿 (PDC) 控制器. 基于 PFLF 方法, 得到了线性矩阵不等式 (LMI) 形式的模糊系统分析与设计的求解方法. 该方法继承了 FLF 与 PQLF 的优点. 仿真实例表明: 该方法所得稳定性判据更为宽松, 具有更好的保性能控制效果. 相似文献
13.
This paper focuses on the problem of fuzzy control for a class of continuous-time T-S fuzzy systems.New methods of stabilization design and H infinity control are derived based on a relaxed approach in... 相似文献
14.
Switching fuzzy controller design based on switching Lyapunov function for a class of nonlinear systems 总被引:4,自引:0,他引:4
Ohtake H. Tanaka K. Wang H.O. 《IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics》2006,36(1):13-23
This paper presents a switching fuzzy controller design for a class of nonlinear systems. A switching fuzzy model is employed to represent the dynamics of a nonlinear system. In our previous papers, we proposed the switching fuzzy model and a switching Lyapunov function and derived stability conditions for open-loop systems. In this paper, we design a switching fuzzy controller. We firstly show that switching fuzzy controller design conditions based on the switching Lyapunov function are given in terms of bilinear matrix inequalities, which is difficult to design the controller numerically. Then, we propose a new controller design approach utilizing an augmented system. By introducing the augmented system which consists of the switching fuzzy model and a stable linear system, the controller design conditions based on the switching Lyapunov function are given in terms of linear matrix inequalities (LMIs). Therefore, we can effectively design the switching fuzzy controller via LMI-based approach. A design example illustrates the utility of this approach. Moreover, we show that the approach proposed in this paper is available in the research area of piecewise linear control. 相似文献
15.
A Sum-of-Squares Approach to Modeling and Control of Nonlinear Dynamical Systems With Polynomial Fuzzy Systems 总被引:3,自引:0,他引:3
《Fuzzy Systems, IEEE Transactions on》2009,17(4):911-922
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Further studies on LMI-based relaxed stabilization conditions for nonlinear systems in Takagi-Sugeno's form 总被引:2,自引:0,他引:2
This paper further studies stabilization of nonlinear systems represented by a Takagi-Sugeno (T-S) discrete fuzzy model. By extending a nonquadratic Lyapunov function and applying a nonparallel distributed compensation (non-PDC) law, a new stabilization conclusion is presented that is a generalization of some previous results in the literature. The new conclusion under a special situation is also suitable for a PDC law, which presents to be more relaxed than some existing results. An example is provided to demonstrate the effectiveness of the new conclusions. 相似文献
17.
输入采用一般模糊划分的T-S模糊控制系统稳定性分析 总被引:4,自引:0,他引:4
通过定义一种对输入空间的一般模糊划分(General fuzzy partition, GFP), 研究了输入采用GFP的T-S模糊系统的性质, 以充分利用规则前件变量的结构信息. 通过构造连续分段光滑Lyapunov函数, 提出了新的T-S模糊控制系统的稳定性条件. 该条件同时考虑了各局部子系统之间的相互关系, 降低了现有稳定性条件的保守性和求解难度. 通过严格证明和数值示例, 比较了所得稳定性条件之间的保守性关系及其与以往充分条件之间的关系. 对运用并行分布补偿(Parallel distributed compensation, PDC)和线性矩阵不等式(Linear matrix inequalities, LMI)方法所设计的T-S模糊控制系统进行计算机仿真研究, 结果验证了所得稳定性条件的有效性和优越性. 相似文献
18.
The proportional parallel distributed compensation (PPDC) approach is utilized to stabilize time‐delay systems modeled by Takagi‐Sugeno fuzzy models in this article. Based on the Lyapunov stability analysis, stability conditions concerning asymptotical stability of time‐delay systems are established. The main advantage of the PPDC approach over the parallel distributed compensation (PDC) approach is that fewer adjustable parameters are needed to ensure stability. Moreover, the procedure of finding common matrices P and S is simplified and the number of Lyapunov inequalities is reduced significantly. The entire PPDC design procedure employing linear matrix inequalities (LMIs) is presented. A numerical example of stabilizing a continuous stirred tank reactor (CSTR) is given to illustrate salient features of the new approach. © 2002 Wiley Periodicals, Inc. 相似文献
19.
Piecewise quadratic stability of fuzzy systems 总被引:10,自引:0,他引:10
Presents an approach to stability analysis of fuzzy systems. The analysis is based on Lyapunov functions that are continuous and piecewise quadratic. The approach exploits the gain-scheduling nature of fuzzy systems and results in stability conditions that can be verified via convex optimization over linear matrix inequalities. Examples demonstrate the many improvements over analysis based on a single quadratic Lyapunov function. Special attention is given to the computational aspects of the approach and several methods to improve the computational efficiency are described 相似文献
20.
This study presents a kind of fuzzy robustness design for nonlinear time-delay systems based on the fuzzy Lyapunov method, which is defined in terms of fuzzy blending quadratic Lyapunov functions. The basic idea of the proposed approach is to construct a fuzzy controller for nonlinear dynamic systems with disturbances in which the delay-independent robust stability criterion is derived in terms of the fuzzy Lyapunov method. Based on the robustness design and parallel distributed compensation (PDC) scheme, the problems of modeling errors between nonlinear dynamic systems and Takagi–Sugeno (T–S) fuzzy models are solved. Furthermore, the presented delay-independent condition is transformed into linear matrix inequalities (LMIs) so that the fuzzy state feedback gain and common solutions are numerically feasible with swarm intelligence algorithms. The proposed method is illustrated on a nonlinear inverted pendulum system and the simulation results show that the robustness controller cannot only stabilize the nonlinear inverted pendulum system, but has the robustness against external disturbance. 相似文献