Delay-Dependent H2/H∞ Control for a Class of Switched T-S Fuzzy Systems with Time-Delay

Delay-dependent H2/H∞ control is studied for a class of switched T-S fuzzy systems. The sufficient condition for delay-dependent asymptotical stability H2 and H∞ and performance of the closed-loop switched T-S fuzzy system are derived. Meanwhile, a switching law and fuzzy controller are designed respectively. Moreover, an optimal problem corresponding with time-delay is provided, and an upper bound of time-delay which ensures the system asymptotically stable is obtained using employing MatLab LMI toolbox. Finally, the effectiveness of the proposed method is demonstrated by a numerical example.

Download Full-text

Observer-Based Control of a Class of Switched Fuzzy Systems

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.945-949.2539 ◽

2014 ◽

Vol 945-949 ◽

pp. 2539-2542

Author(s):

Hong Yang ◽

Huan Huan Lü ◽

Le Zhang

Keyword(s):

Fuzzy System ◽

Fuzzy Systems ◽

Function Method ◽

State Feedback ◽

Closed Loop ◽

External Disturbance ◽

Asymptotically Stable ◽

Closed Loop System ◽

Lyapunov Function Method ◽

Switching State

For the non-measurable states, a control of switched fuzzy systems is presented based on observer. Using switching technique and multiple Lyapunov function method, the fuzzy observer is built to ensure that for all allowable external disturbance the relevant closed-loop system is asymptotically stable. Moreover, switching strategy achieving system global asymptotic stability of the switched fuzzy system is given. In this model, a switching state feedback controller is presented. A simulation shows the feasibility and the effectiveness of the method.

Download Full-text

Design of Output Feedback Controller for Switched Fuzzy Systems with Time-Delay

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.635-637.1443 ◽

2014 ◽

Vol 635-637 ◽

pp. 1443-1446

Author(s):

Hong Yang ◽

Huan Huan Lü ◽

Le Zhang

Keyword(s):

Time Delay ◽

Output Feedback ◽

Fuzzy Systems ◽

Closed Loop ◽

Feedback Controller ◽

Linear Matrix ◽

Sufficient Condition ◽

Closed Loop System ◽

Output Feedback Controller ◽

And Control

This paper investigates the problems of stabilization and control for time-delay switched fuzzy systems using output feedback controller. Based on the linear matrix inequality (LMI) technique, multiple Lyapunov method is used to obtain a sufficient condition for the existence of the controller for the output feedback. Then an algorithm is constructed to transform the sufficient condition into a LMI form, thus obtaining a method for designing the controller. The designed controller guarantees the closed-loop system to be asympototically stable. A numerical example is given to show the effectiveness of our method.

Download Full-text

Global non-quadratic Lyapunov-based stabilization of T–S fuzzy systems: A descriptor approach

Journal of Vibration and Control ◽

10.1177/1077546320904817 ◽

2020 ◽

Vol 26 (19-20) ◽

pp. 1765-1778

Author(s):

Navid Vafamand

Keyword(s):

Stability Analysis ◽

Lyapunov Function ◽

Global Stability ◽

Fuzzy System ◽

Fuzzy Systems ◽

Closed Loop ◽

Fuzzy Controller ◽

Performance Criteria ◽

Membership Functions ◽

Quadratic Lyapunov Function

This article studies the problem of global stability of the Takagi–Sugeno fuzzy systems based on a novel descriptor-based non-quadratic Lyapunov function. A modified non-quadratic Lyapunov function, which comprises an integral term of the membership functions, and a modified non-parallel distributed controller constructed by constant delayed premise variables are considered that assure the global stability of the closed-loop T–S fuzzy system. The special structure of the used non-quadratic Lyapunov function results in time-delayed terms of the membership functions, instead of appearing their time derivatives, which is the well-known issue of the common non-quadratic Lyapunov functions in the literature. Also, the memory fuzzy controller is chosen such that the artificial constant delay-dependent stability analysis conditions for a non-delayed closed-loop T–S fuzzy system are formulated in terms of linear matrix inequalities. To further reduce the conservatives, some slack matrices are introduced by deploying the descriptor representation and decoupling lemmas. Moreover, the design of the robust fuzzy controller is studied through the [Formula: see text] performance criteria. The main advantages of the proposed approach are its small conservatives and the global stability analysis, which distinguish it from the state-of-the-art methods. To show the merits of the proposed approach, comparison results are provided, and two numerical case studies, namely, flexible joint robot and two-link joint robot are considered.

Download Full-text

ANTICONTROL OF CHAOS FOR A CONTINUOUS-TIME TAKAGI–SUGENO FUZZY SYSTEM VIA LOCAL TIME-DELAY FEEDBACK

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127405014362 ◽

2005 ◽

Vol 15 (12) ◽

pp. 3883-3894 ◽

Cited By ~ 2

Author(s):

TAEK RYONG KIM ◽

YOUNG HOON JOO ◽

JIN BAE PARK ◽

GUANRONG CHEN

Keyword(s):

Time Delay ◽

Discrete Time ◽

Continuous Time ◽

Fuzzy System ◽

Closed Loop ◽

Fuzzy Controller ◽

Design Method ◽

Fuzzy Model ◽

Takagi Sugeno ◽

Systematic Control

In this paper, a simple and systematic control design method is proposed for making a continuous-time Takagi–Sugeno (T–S) fuzzy system chaotic. The concept of parallel distributed compensation is employed to determine the structure of a fuzzy controller from a T–S fuzzy model. The fuzzy controller makes the T–S fuzzy model, which could be stable or unstable, bounded and chaotic. The verification of chaos in the closed-loop T–S fuzzy system is done by the following procedure. First, we establish an asymptotically approximate relationship between a continuous-time T–S fuzzy system with time-delay and a discrete-time T–S fuzzy system. Then, we verify the chaos in the closed-loop T–S fuzzy system by applying the Marotto theorem to its associated discrete-time T–S fuzzy system. The generated chaos is in the sense of Li and Yorke. Two examples are given to show that this methodology is simple and effective for anticontrol of chaos for a continuous-time T–S fuzzy system.

Download Full-text

Output Feedback Control for a Class of Switched Fuzzy Systems

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.536-537.1170 ◽

2014 ◽

Vol 536-537 ◽

pp. 1170-1173

Author(s):

Hong Yang ◽

Huan Huan Lü ◽

Le Zhang

Keyword(s):

Feedback Control ◽

Output Feedback ◽

Fuzzy Systems ◽

Closed Loop ◽

Sufficient Conditions ◽

Output Feedback Control ◽

Loop System ◽

Asymptotically Stable ◽

Closed Loop System ◽

Switching Law

The output feedback control problem is addressed for a class of switched fuzzy Systems. Using multiple Lyapunov function method and switching law, the relevant closed-loop system is asymptotically stable, with the switching law designed to implement the global asymptotic stability. The sufficient conditions to ensure the output feedback asymptotically stable output feedback control of closed-loop system are studied. The sufficient condition is transformed into Linear Matrix Inequality (LMI) problem which are more solvable. Finally, a numerical simulation example is employed to illustrate the effectiveness and the convergence of the design methodologies.

Download Full-text

Switching Control for a Class of Switched Fuzzy Systems

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.945-949.2547 ◽

2014 ◽

Vol 945-949 ◽

pp. 2547-2550

Author(s):

Hong Yang ◽

Huan Huan Lü ◽

Le Zhang

Keyword(s):

Fuzzy System ◽

Fuzzy Systems ◽

Function Method ◽

Closed Loop ◽

Switching Control ◽

Asymptotically Stable ◽

Closed Loop System ◽

Main Condition ◽

Switching Strategy ◽

Lyapunov Function Method

A switching control of uncertain switched fuzzy systems is presented. In this model, each subsystem of switched system is an uncertain fuzzy system. Using Multiple Lyapunov function method and switching technique, the relevant closed-loop system is asymptotically stable for all allowable uncertainties. Moreover, switching strategy achieving system global asymptotic stability of the uncertain switched fuzzy system is given. The main condition is given in form of LMI which are more solvable. A simulation shows the feasibility and the effectiveness of the method.

Download Full-text

Stabilization Control with Optimal L1-Gain and L∞-Gain for Positive T-S Fuzzy Systems

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488519500399 ◽

2019 ◽

Vol 27 (06) ◽

pp. 881-903

Author(s):

Jiaxian Wang ◽

Junmin Li

Keyword(s):

Fuzzy Systems ◽

Closed Loop ◽

Fuzzy Controller ◽

Fuzzy Model ◽

Positive System ◽

Asymptotically Stable ◽

Closed Loop System ◽

Stabilization Control ◽

Static Output ◽

Theoretical Results

In this paper, the problem of stabilization with optimal L1-gain for positive T-S fuzzy systems is investigated with the use of linear Lyapunov function. A T-S fuzzy model for positive nonlinear system is established to study the stabilization control for the positive system. Sufficient condition for stabilization is presented in term of linear programming. The static output-feedback fuzzy controller is constructed to guarantee that the closed-loop system is controlled positive, asymptotically stable and the L1-gains from the exogenous inputs to the regulated output is minimized, respectively. Moreover, the stabilization problem with optimal L∞-gain for positive T-S fuzzy systems is solved. Finally, three examples are presented to show the effectiveness of the theoretical results.

Download Full-text

DESIGN OF STATE ESTIMATOR FOR SWITCHED HOPFIELD NEURAL NETWORKS WITH TIME-DELAY

Journal of Circuits System and Computers ◽

10.1142/s0218126611007529 ◽

2011 ◽

Vol 20 (04) ◽

pp. 657-666

Author(s):

CHOON KI AHN

Keyword(s):

Neural Networks ◽

Time Delay ◽

Estimation Error ◽

Hopfield Neural Networks ◽

Linear Matrix ◽

Asymptotically Stable ◽

State Estimator ◽

Error System ◽

Delay Dependent ◽

Dependent State

In this paper, the delay-dependent state estimation problem for switched Hopfield neural networks with time-delay is investigated. Based on the Lyapunov–Krasovskii stability theory, a new delay-dependent state estimator for switched Hopfield neural networks is established to estimate the neuron states through available output measurements such that the estimation error system is asymptotically stable. The gain matrix of the proposed estimator is characterized in terms of the solution to a linear matrix inequality (LMI), which can be checked readily by using some standard numerical packages. An illustrative example is given to demonstrate the effectiveness of the proposed state estimator.

Download Full-text

Robust Stability Analysis of Delay-Dependence for a Class of Switched Uncertain Systems with Time Delay

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.415.139 ◽

2013 ◽

Vol 415 ◽

pp. 139-142

Author(s):

Chi Jo Wang ◽

Juing Shian Chiou

Keyword(s):

Time Delay ◽

Stability Margin ◽

Uncertain System ◽

Switching Law ◽

Delay Dependence ◽

Robust Stability Analysis ◽

Exponentially Stable ◽

Delay Dependent ◽

Interval Systems ◽

Delay Dependent Stability

Some new criteria of delay-dependent stability for the switched time-delay uncertain system are deduced by employing time-switched method and the comparison theorem in this paper. The total activation time ratio of the switching law can be determined to guarantee the switched time-delay uncertain system is exponentially stable with stability margin . Finally, this method can be extended to switched interval systems with time-delay. Some examples are exploited to illustrate the proposed schemes..

Download Full-text