Relaxed stabilization conditions for continuous-time Takagi-Sugeno fuzzy control systems

This paper deals with the stabilization of continuous-time Takagi-Sugeno (T-S) fuzzy control systems. Based on fuzzy Lyapunov functions and nonparallel distributed compensation (non-PDC) control laws, new stabilization conditions are represented in the form of linear matrix inequalities (LMIs). The theoretical proof shows that the proposed conditions can provide less conservatism than the existing results in the literature. Moreover, in order to demonstrate the effectiveness of the non-PDC control laws, the problem of H_∞ controller design for T-S fuzzy systems is also studied. Simulation examples are given to illustrate the merits of the proposed methods.     

离散T-S模糊广义系统的H∞控制

研究了离散T-S模糊广义系统的H_∞控制问题. 首先引入辅助矩阵变量得到新的容许性条件, 解决了由于矩阵P的不定性, 无法运用Schur补引理处理非线性Lyapunov不等式的问题, 进而得到严格不等式表示的H_∞控制条件.基于模糊Lyapunov函数方法, 分别研究了状态反馈控制器、静态输出反馈控制器、动态输出反馈控制器的构造方法. 所得结论可推广到系统具有范数有界不确定性的情况. 最后通过算例验证方法的有效性.     

Quadratic-Stability Analysis of Fuzzy-Model-Based Control Systems Using Staircase Membership Functions

This paper presents the stability analysis of fuzzy-model-based (FMB) control systems. Staircase membership functions are introduced to facilitate the stability analysis. Through the staircase membership functions approximating those of the fuzzy model and fuzzy controller, the information of the membership functions can be brought into the stability analysis. Based on the Lyapunov-stability theory, stability conditions in terms of linear-matrix inequalities (LMIs) are derived in a simple and easy-to-understand manner to guarantee the system stability. The proposed stability-analysis approach offers a nice property that includes the membership functions of both fuzzy model and fuzzy controller in the LMI-based stability conditions for a dedicated FMB control system. Furthermore, the proposed stability-analysis approach can be applied to the FMB control systems of which the membership functions of both fuzzy model and fuzzy controller are not necessarily the same. Greater design flexibility is allowed to choose the membership functions during the design of fuzzy controllers. By employing membership functions with simple structure, it is possible to lower the structural complexity and the implementation cost. Simulation examples are given to illustrate the merits of the proposed approach.      

H/sub /spl infin// controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities

This work presents an H/sub /spl infin// controller design method for fuzzy dynamic systems based on techniques of piecewise smooth Lyapunov functions and bilinear matrix inequalities. It is shown that a piecewise continuous Lyapunov function can be used to establish the global stability with H/sub /spl infin// performance of the resulting closed-loop fuzzy control systems and the control laws can be obtained by solving a set of bilinear matrix inequalities (BMIs). Two examples are given to illustrate the application of the proposed methods.     

H∞ CONTROL FOR DELAYED DISCRETE FUZZY SYSTEMS

In this paper, the H∞ controller design for discrete‐time fuzzy systems with time‐delay is investigated. An improved Lyapunov‐ Krasovskii function which is explicitly dependent on the membership functions is proposed to obtain less conservative results. The controller design problem can be cast into a set of linear matrix inequalities. Finally, a simulation example is given to show the effectiveness of the proposed design approaches.     

Feedback stabilization of fuzzy systems via linear matrix inequalities

This paper considers the problem of designing robust feedback stabilization controller for a class of fuzzy systems. Based on piecewise Lyapunov functions, new design techniques for state feedback and output feedback controllers are proposed. The resultant controller is robust against measurement and modelling perturbations. The design conditions are non-conservative, and the design process is easy to construct by using commercially supported linear matrix inequalities software packages.     

Switching fuzzy controller design based on switching Lyapunov function for a class of nonlinear systems

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.     

Relaxed delay-dependent stabilization criteria for discrete-time fuzzy systems based on a switching fuzzy model and piecewise Lyapunov functions

This paper presents delay-dependent stability analysis and controller synthesis methods for discrete-time Takagi-Sugeno （T-S） fuzzy systems with time delays. The T-S fuzzy system is transformed to an equivalent switching fuzzy system. Consequently, the delay-dependent stabilization criteria are derived for the switching fuzzy system based on the piecewise Lyapunov function. The proposed conditions are given in terms of linear matrix inequalities （LMIs）. The interactions among the fuzzy subsystems are considered in each subregion, and accordingly the proposed conditions are less conservative than the previous results. Since only a set of LMIs is involved, the controller design is quite simple and numerically tractable. Finally, a design example is given to show the validity of the proposed method.     

Dynamic output feedback controller design for fuzzy systems

This paper presents dynamic output feedback controller design for fuzzy dynamic systems. Three kinds of controller design methods are proposed based on a smooth Lyapunov function or a piecewise smooth Lyapunov function. The controller design involves solving a set of linear matrix inequalities (LMI's) and the control laws are numerically tractable via LMI techniques. The global stability of the closed-loop fuzzy control system is also established.     

不确定模糊Delta算子系统的鲁棒H∞控制

研究了一类T-S模糊Delta算子系统的鲁棒H_∞控制问题.首先利用LMI形式给出了模糊Delta算子系统鲁棒镇定的充分条件,然后构造了可使闭环系统鲁棒稳定且对可允许的参数变化满足H_∞性能的状态反馈控制律.本文结果统一了连续与离散模糊系统的鲁棒H_∞镇定设计结论,数值算例说明了方法的可行性.     

Robust H∞ static output‐feedback control for discrete‐time fuzzy systems with actuator saturation via fuzzy Lyapunov functions

In this paper, we present a new scheme for designing a H_∞ stabilizing controller for discrete‐time Takagi‐Sugeno fuzzy systems with actuator saturation and external disturbances. The weighting‐dependent Lyapunov functions approach is used to design a robust static output‐feedback controller. To address the input saturation problem, both constrained and saturated control input cases are considered. In both cases, stabilization conditions of the fuzzy system are formulated as a convex optimization problem in terms of linear matrix inequalities. Two simulation examples are included to illustrate the effectiveness of the proposed design methods. A comparison with the results given in recent literature on the subject is also presented.     

Finite‐Time Stabilization of a Class of Cascade Nonlinear Switched Systems

This paper investigates the finite‐time stabilization problem for a class of cascade nonlinear switched systems. Using the average dwell time and multiple Lyapunov function technologies, some sufficient conditions to guarantee that the corresponding closed‐loop system is finite‐time stabilized are derived for the switched systems. Via multiple Lyapunov functions, the state feedback controller is designed to finite‐time stabilize a cascade nonlinear switched system, and the conditions are formulated in terms of linear matrix inequalities. An example is given to illustrate the efficiency of the proposed methods.     

Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.     

NON‐PDC Observer‐Based T‐S Fuzzy Tracking Controller Design and its Application in CHAOS Control

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.     

H-infinity performance optimization for networked control systems with limited communication channels

This paper studies the problems of H-infinity performance optimization and controller design for continuoustime NCSs with both sensor-to-controller and controller-to-actuator communication constraints (limited communication channels). By taking the derivative character of network-induced delay into full consideration and defining new Lyapunov functions, linear matrix inequalities (LMIs)-based H-infinity performance optimization and controller design are presented for NCSs with limited communication channels. If there do not exist any constraints on the communication channels, the proposed design methods are also applicable. The merit of the proposed methods lies in their less conservativeness, which is achieved by avoiding the utilization of bounding inequalities for cross products of vectors. The simulation results illustrate the merit and effectiveness of the proposed H-infinity controller design for NCSs with limited communication channels.     

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.     

模糊动态系统的H∞输出反馈控制设计——应用线性矩阵不等式的算法

讨论了一类能用模糊动态系统模型表示的非线性系统的H∞输出反馈控制的设计. 分别基于一个共同的李亚普诺夫方程和一个分段微分的李亚普诺夫方程,给出了两种H∞ 输出反馈模糊控制的新设计方法.通过解一组线性矩阵不等式,可以得到H∞输出反馈控 制器.最后,举例说明了这两种新的设计方法.     

Robust tracking control for uncertain fuzzy systems with time delay and external disturbances

In this article, robust tracking and disturbance rejection problem for Takagi–Sugeno fuzzy systems with time delay and external disturbances are discussed. Specifically, proportional-integral controller with an enhanced equivalent-input-disturbance technique is constructed to force the output trajectories to track the bounded reference input signal even in the presence of external disturbances. Further, the resulting fuzzy control system can be represented as an augmented system with state delay and uncertainties and the output tracking problem is transformed into stabilization problem of the augmented system. In the stabilization analysis, the considered fuzzy system does not share the same membership functions with the proposed control. Moreover, the delay-dependent stabilization criteria for the addressed fuzzy system are presented in the form of linear matrix inequalities by the virtue of augmented Lyapunov–Krasovskii functional. To be specific, the symmetric matrices involved in the Lyapunov–Krasovskii functional need not be positive definite. Ultimately, three numerical examples are offered to support the validity of the established theoretical results.     

Robust H-infinity fuzzy control for uncertainMarkovian jump nonlinear singular systems withwiener process

This paper deals with the problems of robust stochastic stabilization and H-infinity control for Markovian jump nonlinear singular systems with Wiener process via a fuzzy-control approach. The Takagi-Sugeno (T-S) fuzzy model is employed to represent a nonlinear singular system. The purpose of the robust stochastic stabilization problem is to design a state feedback fuzzy controller such that the closed-loop fuzzy system is robustly stochastically stable for all admissible uncertainties. In the robust H-infinity control problem, in addition to the stochastic stability requirement, a prescribed performance is required to be achieved. Linear matrix inequality (LMI) sufficient conditions are developed to solve these problems, respectively. The expressions of desired state feedback fuzzy controllers are given. Finally, a numerical simulation is given to illustrate the effectiveness of the proposed method.