scholarly journals Guaranteed Cost Control Design of 4D Lorenz-Stenflo Chaotic System via T-S Fuzzy Approach

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Yi-You Hou ◽  
Meei-Ling Hung ◽  
Jui-Sheng Lin
Keyword(s):  
Chaotic System ◽  
State Feedback ◽  
Cost Control ◽  
Lyapunov Stability Theory ◽  
Guaranteed Cost Control ◽  
Linear Matrix ◽  
Control Of Chaos ◽  
Guaranteed Cost ◽  
Takagi Sugeno ◽  
Method Approach

This paper investigates the guaranteed cost control of chaos problem in 4D Lorenz-Stenflo (LS) system via Takagi-Sugeno (T-S) fuzzy method approach. Based on Lyapunov stability theory and linear matrix inequality (LMI) technique, a state feedback controller is proposed to stabilize the 4D Lorenz-Stenflo chaotic system. An illustrative example is provided to verify the validity of the results developed in this paper.

scholarly journals Controlling Chaos in Permanent Magnet Synchronous Motor Control System via Fuzzy Guaranteed Cost Controller

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Yi-You Hou
Keyword(s):  
Permanent Magnet ◽  
Permanent Magnet Synchronous Motor ◽  
Lyapunov Stability Theory ◽  
Synchronous Motor ◽  
Linear Matrix ◽  
Control Of Chaos ◽  
Guaranteed Cost ◽  
Motor Control System ◽  
Takagi Sugeno ◽  
Method Approach

This paper investigates the guaranteed cost control of chaos problem in permanent magnet synchronous motor (PMSM) via Takagi-Sugeno (T-S) fuzzy method approach. Based on Lyapunov stability theory and linear matrix inequality (LMI) technique, a state feedback controller is proposed to stabilize the PMSM systems. An illustrative example is provided to verify the validity of the results developed in this paper.

OPTIMAL GUARANTEED COST CONTROL OF UNCERTAIN STOCHASTIC COMPLEX DELAYED DYNAMICAL NETWORKS

2010 ◽  
Vol 10 (04) ◽  
pp. 577-590 ◽  
Author(s):  
SHUKAI LI ◽  
WANSHENG TANG ◽  
JIANXIONG ZHANG
Keyword(s):  
Complex Networks ◽  
State Feedback ◽  
Cost Control ◽  
Guaranteed Cost Control ◽  
Linear Matrix ◽  
Feedback Controllers ◽  
Control Laws ◽  
Guaranteed Cost ◽  
Stochastic Complex Networks ◽  
Delayed Dynamical Networks

This paper investigates the optimal guaranteed cost control of synchronization for uncertain stochastic complex networks with time-varying delays. The aim is to design state-feedback controllers such that the complex networks are globally asymptotical mean-square synchronization, and meanwhile the optimal upper bound of cost function is guaranteed. Based on Lyapunov–Krasovskii stability theory and Itô differential rule, sufficient condition for the existence of the optimal guaranteed cost control laws is given in terms of linear matrix inequalities (LMIs). A numerical example is given to illustrate the effectiveness of the proposed method.

Delay-dependent guaranteed cost control for a non-linear stochastic system with distributed delays

2009 ◽  
Vol 223 (6) ◽  
pp. 763-772 ◽  
Author(s):  
J Qiu ◽  
H He ◽  
P Shi
Keyword(s):  
Stochastic Systems ◽  
Cost Control ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Guaranteed Cost Control ◽  
Linear Matrix ◽  
Guaranteed Cost ◽  
Non Linear ◽  
Delay Dependent ◽  
Delay Dependent Stability

In this paper, the problem of guaranteed cost control for stochastic systems is considered. The system is non-linear, and the delays are distributed. Based on Lyapunov stability theory combined with the linear matrix inequality (LMI) technique, delay-dependent stability and stabilization conditions are proposed. Furthermore, sufficient conditions for the existence of guaranteed cost controllers are derived. Finally, a numerical example is used to illustrate the effectiveness and feasibility of the approaches proposed in this paper.

Guaranteed Cost Control for a Class of Switched Descriptor Systems

2012 ◽  
Vol 546-547 ◽  
pp. 1030-1034
Author(s):  
Chun Yuan Zhao ◽  
Shu Hui Shi
Keyword(s):  
State Feedback ◽  
Cost Control ◽  
Convex Combination ◽  
Guaranteed Cost Control ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Combination Technique ◽  
Switching Law ◽  
Guaranteed Cost

This paper deals with the problem of guaranteed cost control for a class of switched descriptor systems. State feedback guaranteed cost controller is adopted to make the resulting closed-loop system stable and cost function have an upper bound. Based on single Lyapunov function and convex combination technique, a switching law is designed and a sufficient condition of the existence of such controller is presented. By means of variables substitution and linear matrix inequality, the condition can be turned to LMI. The advantage of method presented in this paper is illustrated by an example.

Non-Fragile Guaranteed Cost Control for a Class of Uncertain Time-Delay Switched Singular Systems

2013 ◽  
Vol 380-384 ◽  
pp. 639-647
Author(s):  
Yue Sheng Luo ◽  
Man Xu ◽  
Shi Lei Zhang ◽  
Tong Li ◽  
Chun Fang Liu
Keyword(s):  
Time Delay ◽  
Cost Control ◽  
Singular Systems ◽  
Singular System ◽  
Guaranteed Cost Control ◽  
Feasibility Problem ◽  
Linear Matrix ◽  
Cost Index ◽  
Guaranteed Cost ◽  
Uncertain Time

The problem of robustly non-fragile guaranteed cost control for a class of uncertain time-delay switched singular systems under arbitrary switching laws is considered. By means of matrix equivalent transformation and the relationship between the norm and the matrix, based on linear matrix inequality tools, a sufficient condition on the existence of non-fragile guaranteed cost state feedback controllers is derived, which ensures that uncertain time-delay switched singular system is admissible, and a corresponding cost index can be guaranteed. The design problem of the non-fragile guaranteed cost controller can be turned into the feasibility problem of a set of linear matrix inequalities. Finally, an illustrative example is given to demonstrate the effectiveness of proposed method.

An LMI approach to non-fragile robust optimal guaranteed cost control of uncertain 2-D discrete systems with both state and input delays

2016 ◽  
Vol 40 (3) ◽  
pp. 785-804 ◽  
Author(s):  
Akshata Tandon ◽  
Amit Dhawan
Keyword(s):  
Cost Control ◽  
Discrete Systems ◽  
Guaranteed Cost Control ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Parameter Uncertainties ◽  
Convex Optimization Problem ◽  
Guaranteed Cost ◽  
State And Input Delays ◽  
Input Delays

In this paper, we present a solution to the problem of non-fragile robust optimal guaranteed cost control for a class of uncertain two-dimensional(2-D) discrete systems described by the general model (GM) subject to both state and input delays. The parameter uncertainties are assumed norm-bounded. A linear matrix inequality (LMI)-based sufficient condition for the existence of non-fragile robust guaranteed cost controller is established. Furthermore, a convex optimization problem with LMI constraints is proposed to select a non-fragile robust optimal guaranteed cost controller stabilizing the uncertain 2-D discrete system with both state and input delays as well as achieving the least guaranteed cost for the resulting closed-loop system. The effectiveness of the proposed method is demonstrated with an illustrative example.

Guaranteed Cost Control for Fuzzy Bilinear Systems with Uncertain Parameters

2012 ◽  
Vol 433-440 ◽  
pp. 1723-1729
Author(s):  
Ze Feng Gao ◽  
Jun Chen ◽  
Fei Liu
Keyword(s):  
Cost Control ◽  
Fuzzy Controller ◽  
Sufficient Conditions ◽  
Schur Complement ◽  
Guaranteed Cost Control ◽  
Bilinear Systems ◽  
Linear Matrix ◽  
Main Theme ◽  
Control Laws ◽  
Guaranteed Cost

The main theme of this paper is to present robust guaranteed cost control laws for a class of fuzzy bilinear systems (FBS) with parametric uncertainties. First, the piecewise Lyapunov function (PLF) method is utilized to design a fuzzy controller, which ensures the robust asymptotic stability of the closed-loop system, and then the robust guaranteed cost control law is also proposed. Second, based on the Schur complement and some variable transformations, some sufficient conditions are derived to guarantee the stability of the overall fuzzy control system via linear matrix inequalities (LMIs). Finally, a numerical example is utilized to demonstrate the validity and effectiveness of the proposed control scheme.

Guaranteed Cost Control of State-Delay System Based on the Equivalent-Input-Disturbance Approach

2016 ◽  
Vol 20 (2) ◽  
pp. 246-253
Author(s):  
Fang Gao ◽  
◽  
Min Wu ◽  
Jinhua She ◽  
Pan Yu ◽  
...  
Keyword(s):  
Linear Matrix Inequality ◽  
Cost Control ◽  
Guaranteed Cost Control ◽  
Delay System ◽  
Linear Matrix ◽  
Control Law ◽  
Matrix Inequality ◽  
State Delay ◽  
Input Disturbance ◽  
Guaranteed Cost

This paper considers a guaranteed cost control problem for state-delay systems with exogenous disturbances for a proper plant. The equivalent-input-disturbance (EID) approach is extended to be able to handle a state-delay system. A new control law is constructed that incorporates an EID estimate in order to ensure a satisfactory control performance. A stability condition for the closed-loop system is provided in terms of a linear matrix inequality, using the Lyapunov function method. Furthermore, a guaranteed cost control state feedback control law and a state observer are designed, based on the linear matrix inequality (LMI). Two numerical examples are provided to demonstrate the validity of the method.

Guaranteed Cost Control For Constrained Takagi-Sugeno Fuzzy Systems

2009 ◽  
Vol 42 (19) ◽  
pp. 325-330
Author(s):  
Carlos Ariño ◽  
Emilio Pérez ◽  
Antonio Sala
Keyword(s):  
Fuzzy Systems ◽  
Cost Control ◽  
Guaranteed Cost Control ◽  
Guaranteed Cost ◽  
Takagi Sugeno
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