New Approach to Stability Analysis and Stabilization of Discrete-Time T-S Fuzzy Descriptor Systems

The problems of stability and state feedback control for a class of discrete-time T-S fuzzy descriptor systems are investigated in this paper. Based on fuzzy Lyapunov function,a set of slack variables is introduced to remove the basic semi-definite matrix inequality condition to check the regularity,causality and stability of discrete-time T-S fuzzy descriptor systems; a new sufficient condition for the discrete-time T-S fuzzy descriptor systems to be admissible is proposed in terms of strict linear matrix inequalities( LMIs). And a sufficient condition is proposed for the existence of state feedback controller in terms of a set of coupled strict LMIs.Finally,an illustrative example is presented to demonstrate the effectiveness of the proposed approach.

Stability analysis and controller design of T-S fuzzy systems with time-delay under imperfect premise matching

The issue of the stability and controller design of Takagi-Sugeno（T-S） fuzzy control systems with time-delay is investigated under imperfect premise matching when the T-S fuzzy time-delay model and fuzzy controller do not share the same membership functions.A new stability criterion which contains the information of membership functions is derived.The new stability criterion is less conservative,and enhances the design flexibility.Two numerical examples are presented to illustrate the conservativeness and effectiveness of the proposed method.

Stability analysis of T-S fuzzy control systems with interval plants

The stability of a type of Takagi-Sugeno ( T-S) fuzzy control systems is considered. The plant of T-S fuzzy system has parameter uncertainties. By using the off-axis circle criterion and Kharitonov Theorem,a sufficient condition is derived to analyze the global asymptotic stability of T-S fuzzy control system. The proposed method has a graphical explanation which facilitates stability analysis. A numerical example is also given to demonstrate how to use our approach in analyzing certain T-S fuzzy control systems.

Stability analysis of the simplest Takagi-Sugeno fuzzy control system using circle criterion

A frequency-domain-based sufficient condition is derived to guarantee the globally asymptotic stability of the simplest Takagi-Sugeno （T-S） fuzzy control system by using the circle criterion. The analysis is performed in the frequency domain, and hence the condition is of great significance when the frequency-response method, which is widely used in the linear control theory and practice, is employed to synthesize the simplest T-S fuzzy controller. Besides, this sufficient condition is featured by a graphical interpretation, which makes the condition straightforward to be used. Comparisons are drawn between the performance of the simplest T-S fuzzy controller and that of the linear compensator. Two numerical examples are presented to demonstrate how this sufficient condition can be applied to both stable and unstable plants.

New Stability Condition of T-S Fuzzy Systems and Design of Robust Flight Control Principle

Unlike the previous research works analyzing the stability of the T-S （Takagi-Sugeno） fuzzy model, an extension on the stability condition of T-S fuzzy systems with a different strategy is provided. In the strategy a new variable, which is relative to the grade of fuzzy membership function, is introduced to the stability analysis and a new stability conclusion is deduced. The definition of stability condition in this paper is different from previous works, though they are similar in form. With the proposed method, the simulation in flight control law shows a better effectiveness.

Stability and stabilization of discrete T-S fuzzy time-delay system based on maximal overlapped-rules group

The problems of stability and stabilization for the discrete Takagi-Sugeno（T-S） fuzzy time-delay system are investigated.By constructing a discrete piecewise Lyapunov-Krasovskii function（PLKF） in each maximal overlapped-rules group（MORG）,a new sufficient stability condition for the open-loop discrete T-S fuzzy time-delay system is proposed and proved.Then the systematic design of the fuzzy controller is investigated via the parallel distributed compensation control scheme,and a new stabilization condition for the closed-loop discrete T-S fuzzy time-delay system is proposed.The above two sufficient conditions only require finding common matrices in each MORG.Compared with the common Lyapunov-Krasovskii function（CLKF） approach and the fuzzy Lyapunov-Krasovskii function（FLKF） approach,these proposed sufficient conditions can not only overcome the defect of finding common matrices in the whole feasible region but also largely reduce the number of linear matrix inequalities to be solved.Finally,simulation examples show that the proposed PLKF approach is effective.

Design of TakagiSugeno fuzzy model based nonlinear sliding model controller

A design method is presented for Takagi-Sugeno （T-S） fuzzy model based nonlinear sliding model controller. First, the closed-loop fuzzy system is divided into a set of dominant local linear systems according to operating sub-regions. In each sub-region the fuzzy system consists of nominal linear system and a group of interacting systems. Then the controller composed two parts is designed. One part is designed to control the nominal system, the other is designed to control the interacting systems with sliding mode theory. The proposed controller can improve the robusmess and gnarantee tracking performance of the fuzzy system. Stability is guaranteed without finding a common positive definite matrix.

T-S模糊控制系统稳定性分析及控制器设计

研究了在新型的模糊Lyapunov方法下连续T-S模糊控制系统稳定性和模糊控制器设计问题,首先,得出了自由系统新的稳定性充分条件,这个条件具有更大的宽松性;然后基于一系列线性矩阵不等式设计了模糊控制器,这些矩阵不等式可以利用凸优化技术来进行解决。通过对两个具体的实例的仿真验证了本算法的有效性。

连续T-S模糊控制器的稳定性分析与设计

利用矩阵的谱范数估计 ,研究了连续 T- S型模糊控制器的稳定性 ,给出模糊开环系统稳定的充分条件。基于开环系统的稳定性判据 ,提出闭环系统的稳定性条件及设计方法。最后 。

离散T-S模糊控制系统的稳定性分析与系统化设计

研究了离散T-S模糊控制系统的稳定性判定方法和系统化设计方法:在所有的最大交叠规则组中构造出分段离散型Lyapunov函数,每个离散Lyapunov函数是各自最大交叠规则组中的一个Lyapunov函数。在此基础上,提出了一个新的判定系统稳定性的充分条件,该条件仅需在每个最大交叠规则组中分别寻找各自公共的正定矩阵。较之以往稳定性判定方法,此方法不仅克服了需要寻找一个公共矩阵的不足,而且也减少了求解Lyapunov不等式的个数。文中利用并行分布补偿方法设计了模糊控制器,仿真示例说明了此方法的有效性和优越性。

T-S模糊系统输出直接反馈控制器设计

讨论了T-S模糊系统输出直接反馈控制器的稳定性分析和设计方法。为了减小稳定性分析的保守性和难度,充分利用模糊规则前件变量模糊隶属度函数的结构信息,对前件变量采用标准模糊分划的T-S模糊系统输出直接反馈控制器进行了研究,获得了稳定性条件。在稳定性分析的基础上,采用平行分布补偿法(PDC)和线性矩阵不等式方法(LMI),研究了输出直接反馈控制器的设计。通过对一个非线性质量块-弹簧-阻尼器系统输出反馈控制器的设计和计算机仿真,验证了方法的有效性。

T-S模糊系统输出反馈控制器的稳定性分析与设计

输出反馈控制是T-S模糊控制系统设计的一种重要方法．本文提出了一类由模糊状态观测器和模糊调节器构成的输出反馈控制器稳定性分析和解析设计的新方法．为了减小稳定性分析的保守性和难度,本文充分利用了模糊规则前件变量模糊隶属度函数的结构信息,对前件变量采用标准模糊分划的T-S模糊系统输出反馈控制器进行了研究,获得了一些新的稳定性条件．然后采用平行分布补偿法(PDC)和线性矩阵不等式方法(LMI),研究了该类输出反馈控制器的解析设计方法．通过一个非线性质量块-弹簧-阻尼器系统输出反馈控制器的设计和计算机仿真,验证了本文方法的有效性．

Adaptive Fuzzy Observer Backstepping Control for a Class of Uncertain Nonlinear Systems with Unknown Time-delay

In this paper, a new adaptive fuzzy backstepping control approach is developed for a class of nonlinear systems with unknown time-delay and unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the state observer and applying the backstepping technique, an adaptive fuzzy observer control approach is developed. The main features of the proposed adaptive fuzzy control approach not only guarantees that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded, but also contain less adaptation parameters to be updated on-line. Finally, simulation results are provided to show the effectiveness of the proposed approach.

Indirect adaptive fuzzy control for a class of nonlinear discrete-time systems

An indirect adaptive fuzzy control scheme is developed for a class of nonlinear discrete-time systems. In this method, two fuzzy logic systems are used to approximate the unknown functions, and the parameters of membership functions in fuzzy logic systems are adjusted according to adaptive laws for the purpose of controlling the plant to track a reference trajectory. It is proved that the scheme can not only guarantee the boundedness of the input and output of the closed-loop system, but also make the tracking error converge to a small neighborhood of the origin. Simulation results indicate the effectiveness of this scheme.

离散广义T-S模糊系统的稳定性分析

针对广义模糊系统的结构特点和技术要求,构造出离散广义分段模糊Lyapunov函数的处理技术,讨论了输入采用双交叠模糊分化的离散广义T-S模糊系统的稳定性和控制器设计问题,在分段Lyapunov函数的基础上采用并行分布补偿法设计出离散广义模糊系统的模糊控制器,得出了新的判定闭环离散T-S模糊广义系统稳定性的充分条件,即在各最大交叠规则组内寻求一个公共正定矩阵和一个对称矩阵。所提出的条件成功的运用在模糊规则数较多的模糊系统中,取得了明显的效果。数值算例说明此法的有效性。

Comparative Study of Different Decoupling Schemes for TITO Binary Distillation Column via PI Controller

This paper presents a comparative study of different decoupling control schemes for a two-input, two-output(TITO) binary distillation column via proportional-integral(PI)controller. The key idea behind this paper is designing two novel fuzzy decoupling schemes that depend on human knowledge,instead of the system mathematical model used in conventional decoupling schemes. Based on conventional and inverted decoupling schemes, fuzzy and inverted fuzzy decoupling schemes are developed. The control effect is compared using simulation results for the proposed two schemes with conventional decoupling and inverted decoupling. The proposed fuzzy decoupling schemes are easy to realize and simple to design, besides they have a good decoupling capability. Two methods are used to prove asymptotic stability of each loop and the entire closed-loop system by applying the proposed fuzzy decoupling-based PI controller.The Wood and Berry model of a binary distillation column is used to illustrate the applicability of the proposed schemes.

Robust Control for Interval Type-2 T-S Fuzzy Discrete Systems with Input Delays and Cyber Attacks

This paper focuses on the robust control issue for interval type-2 Takagi-Sugeno(IT2 T-S)fuzzy discrete systems with input delays and cyber attacks.The lower and upper membership functions are first utilized to IT2 fuzzy discrete systems to capture parameter uncertainties.By considering the influences of input delays and stochastic cyber attacks,a newly fuzzy robust controller is established.Afterward,the asymptotic stability sufficient conditions in form of LMIs for the IT2 closed-loop systems are given via establishing a Lyapunov-Krasovskii functional.Afterward,a solving algorithm for obtaining the controller gains is given.Finally,the effectiveness of the developed IT2 fuzzy method is verified by a numerical example.

四旋翼无人机改进自抗扰姿态控制

针对四旋翼无人机姿态控制过程中模型不确定及外部扰动问题,设计了一种自抗扰控制的姿态控制器。将模糊控制方法与传统的自抗扰控制理论相结合,增加了一个集模糊化、模糊推理和清晰化为一体的模糊控制单元,采用改进天牛须算法整定自抗扰控制器参数,提高了参数整定效率。为解决fal函数拐点处不平滑,易产生小幅抖振以及误差较大时系统增益较大等问题,引入了改进的yfal函数替代扩张状态观测器中的fal函数,并对改进后的状态观测器进行了收敛性判断。仿真结果表明,改进后的自抗扰控制器具有更快的响应速度和抗干扰能力。

基于模糊理论的输电网络电压无功控制策略

为解决新能源、电动汽车、储能等新技术应用下,高复杂度电力系统电压稳定控制问题,提出了一种基于模糊理论的输电网络电压无功控制策略。该方法引入模糊理论中的隶属度函数,根据系统节点与不同分区之间的耦合程度制定无功控制策略。根据灵敏度计算网络各个节点之间的电气距离,通过模糊聚类算法对节点进行初步分区,并采用聚类融合算法对聚类产生的多个结果进行融合,从而得到最终分区结果。根据关键节点对各个分区的隶属度制定主辅控制策略。IEEE30节点输电网络的算例分析表明,该控制策略可以有效实现对无功功率的控制。

Takagi-Sugeno Fuzzy Regulator Design for Nonlinear and Unstable Systems Using Negative Absolute Eigenvalue Approach

This paper introduces a Takagi-Sugeno(T-S)fuzzy regulator design using the negative absolute eigenvalue(NAE)approach for a class of nonlinear and unstable systems.The open-loop system is initially embodied by the traditional T-S fuzzy model and then,all closed-loop subsystems are combined using the proposed Max-Min operator in place of traditional weighted average operator from the controller side to lessen the coupling virtually and simplify the proposed regulator design.For each virtually decoupled closed-loop subsystem,the composite regulators(i.e.,primary and secondary regulators)are designed by the NAE approach based on the enhanced eigenvalue analysis.The Lyapunov function is utilized to guarantee the asymptotic stability of the overall T-S fuzzy control system.The most popular and widely used nonlinear and unstable systems like the electromagnetic levitation system(EMLS)and the inverted cart pendulum(ICP)are simulated for the wide range of the initial conditions and the enormous variation in the disturbance.The transient and steady-state performance of the considered systems using the proposed design are analyzed in terms of the decay rate,settling time and integral errors as IAE,ISE,ITAE,and ITSE to validate the effectiveness of the proposed approach compared to the most popular and traditional parallel distributed compensation(PDC)approach.