Observer-Based Control of a Class of Switched Fuzzy Systems

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.

Switching Control for a Class of Switched Fuzzy Systems

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.

scholarly journals Boundary stabilization and disturbance rejection for an unstable time fractional diffusion-wave equation

2022 ◽  
Author(s):  
Hua-Cheng Zhou ◽  
Ze-Hao Wu ◽  
Bao-Zhu Guo ◽  
Yangquan Chen
Keyword(s):  
Output Feedback ◽  
Disturbance Rejection ◽  
State Feedback ◽  
Closed Loop ◽  
External Disturbance ◽  
Fractional Diffusion ◽  
Loop System ◽  
Boundary Stabilization ◽  
Closed Loop System ◽  
Diffusion Wave

In this paper, we study boundary stabilization and disturbance rejection problem for an unstable time fractional diffusion-wave equation with Caputo time fractional derivative. For the case of no boundary external disturbance, both state feedback control and output feedback control via Neumann boundary actuation are proposed by the classical backstepping method. It is proved that the state feedback makes the closed-loop system Mittag-Leffler stable and the output feedback makes the closed-loop system asymptotically stable. When there is boundary external disturbance, we propose a disturbance estimator constructed by two infinite dimensional auxiliary systems to recover the external disturbance. A novel control law is then designed to compensate for the external disturbance in real time, and rigorous mathematical proofs are presented to show that the resulting closed-loop system is Mittag-Leffler stable and the states of all subsystems involved are uniformly bounded. As a result, we completely resolve, from a theoretical perspective, two long-standing unsolved mathematical control problems raised in [Nonlinear Dynam., 38(2004), 339-354] where all results were verified by simulations only.

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

2011 ◽  
Vol 204-210 ◽  
pp. 1197-1202 ◽  
Author(s):  
Yue Quan Yang ◽  
Jian Mei Jiang ◽  
Tian Ping Zhang ◽  
Yang Yi ◽  
Qing Zhu
Keyword(s):  
Time Delay ◽  
Fuzzy System ◽  
Fuzzy Systems ◽  
Closed Loop ◽  
Fuzzy Controller ◽  
Sufficient Condition ◽  
Asymptotically Stable ◽  
Switching Law ◽  
And Performance ◽  
Delay Dependent

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.

Further results on adaptive state feedback stabilization for a class of stochastic feedforward nonlinear systems with time delays

2018 ◽  
Vol 41 (1) ◽  
pp. 127-134 ◽  
Author(s):  
Xiaoyan Qin ◽  
Huifang Min
Keyword(s):  
Nonlinear Systems ◽  
Time Delays ◽  
State Feedback ◽  
Closed Loop ◽  
Feedback Stabilization ◽  
Asymptotically Stable ◽  
Closed Loop System ◽  
Transformation Technique ◽  
Globally Asymptotically Stable ◽  
Feedforward Nonlinear Systems

This paper further discusses the state feedback stabilization for stochastic high-order feedforward nonlinear systems with input time delay. By constructing the appropriate Lyapunov–Krasovskii functional, and using the variable transformation technique and the homogeneous domination idea, a state feedback controller is designed to ensure that the closed-loop system will be globally asymptotically stable in probability. Finally, an example is given to verify the effectiveness of the obtained analytical results.

Observer-based event-triggered H∞ control for asynchronous switched delay systems

2020 ◽  
Vol 42 (12) ◽  
pp. 2254-2261
Author(s):  
Yang Yang ◽  
Baowei Wu ◽  
Yue-E Wang ◽  
Lili Liu
Keyword(s):  
State Feedback ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Economic Losses ◽  
System State ◽  
Closed Loop System ◽  
Lyapunov Function Method ◽  
Signal Method ◽  
Event Triggered

In this paper, the [Formula: see text] performance of observer-based asynchronous linear switched delay systems with an event-triggered sampling scheme is considered. Firstly, owing to the system state cannot be measured completely in practice, a state feedback observer is used to reconstruct the system state. Next, we design an event-triggered sampling mechanism, under which the sample of the system only occur when the error exceeds a predetermined threshold, so it will reduce economic losses. Then, considering the asynchronous switching between the subsystems and the controllers, some sufficient conditions are proposed by using merging switching signal method and multiple Lyapunov function method to ensure the [Formula: see text] performance of the asynchronous closed-loop system. Finally, a numerical example is given to illustrate the validity of the results.

Output Feedback Control for a Class of Switched Fuzzy Systems

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.

Controller Design for See-Saw Systems

2014 ◽  
Vol 898 ◽  
pp. 680-683
Author(s):  
Hai Yan Wang
Keyword(s):  
Control Theory ◽  
State Feedback ◽  
Closed Loop ◽  
Controller Design ◽  
The State ◽  
Feedback Controller ◽  
System Model ◽  
Asymptotically Stable ◽  
Closed Loop System ◽  
State Feedback Controller

The control theory has widely application in many fields such as industrial and agricultural. A class of see-saw system model will be studied in this paper. Using the theory of pole assignment, we will design the state feedback controller, such that the closed-loop system is asymptotically stable. At the same time, using the tool of MATLAB, the model of closed see-saw system will be simulated and analyzed. It reveals the state regularity of see-saw system.

Output Feedback Control for a Class of Uncertain Fuzzy System by Controller Switching

2013 ◽  
Vol 397-400 ◽  
pp. 1341-1344
Author(s):  
Huan Huan Lü ◽  
Hong Yang
Keyword(s):  
Output Feedback ◽  
Lyapunov Functions ◽  
Fuzzy Systems ◽  
Closed Loop ◽  
Output Feedback Control ◽  
Asymptotically Stable ◽  
Closed Loop System ◽  
Class Model ◽  
Theoretical Derivation ◽  
Switching Method

Fuzzy control does not have a precise mathematical model, but it is a very effective way to deal with complex systems stability problems. Firstly, a class of uncertain fuzzy systems is given, and in this class model the parallel distributed compensation (PDC) controller switching method is introduced. Next, the methods of single Lyapunov function and multi Lyapunov functions are respectively used to obtain the conditions which make the closed-loop system asymptotically stable. Finally using the MATLAB/SIMULINK software to simulate, verify the feasibility and effectiveness of the theoretical derivation.

An LMI Approach to State Feedback H∞ Control for Switched Singular Linear Systems

2014 ◽  
Vol 875-877 ◽  
pp. 835-840
Author(s):  
Zhu Mu Fu ◽  
Bin Wang ◽  
Ai Yun Gao
Keyword(s):  
Linear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Linear Matrix ◽  
Asymptotically Stable ◽  
Closed Loop System ◽  
Lmi Approach ◽  
Singular Linear Systems

In this paper, the problems of state feedback control for a class of switched singular linear systems are investigated. By constructing a novel switched Lyapunov functional and convex combinations techniques, a sufficient condition established in terms of strict linear matrix inequalities (LMIs) is presented such that the system is asymptotically stable and satisfies performance. An explicit expression for the state feedback stabilization sub-controller and switching rule are designed. The merits of the proposed criteria lie in their less conservativeness and relative simplicity, in which the closed-loop system satisfies performance at each point in whole state-space through switching, although each sub-system doesn’t satisfy the performance and even is not asymptotically stable. A numerical example is provided to illustrate the validity of the proposed methods.

scholarly journals State Feedback Control for Stochastic Feedforward Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Liang Liu ◽  
Ming Gao
Keyword(s):  
Nonlinear Systems ◽  
State Feedback ◽  
Closed Loop ◽  
Feedback Stabilization ◽  
State Feedback Control ◽  
Asymptotically Stable ◽  
Stabilization Problem ◽  
Closed Loop System ◽  
Globally Asymptotically Stable ◽  
Feedforward Nonlinear Systems

This paper considers the state feedback stabilization problem for a class of stochastic feedforward nonlinear systems. By using the homogeneous domination approach, a state feedback controller is constructed to render the closed-loop system globally asymptotically stable in probability. A simulation example is provided to show the effectiveness of the designed controller.

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