Robust H∞ Control for Takagi-Sugeno Fuzzy Systems with Time-Varying Delays in State and Input

2015 ◽  
Vol 764-765 ◽  
pp. 624-628 ◽  
Author(s):  
Shun Hung Tsai ◽  
Siou An Jian
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Fuzzy Systems ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Stabilization Problem ◽  
State And Input Delays ◽  
Input Delays ◽  
Takagi Sugeno

In this paper, the robust H∞ stabilization problem for Takagi-Sugeno fuzzy control systemswith state and input delays is explored. Based on a Lyapunov-Krasoviskii function, the delaydependentstabilization conditions are proposed in terms of linear matrix inequalities (LMIs) to guaranteethe asymptotic stabilization of time-delay Takagi-Sugeno fuzzy systems with disturbance input.Finally, a numerical example is illustrated to demonstrate the feasibility and effectiveness of the proposed stabilization.

scholarly journals Finite frequency model reduction for 2-D fuzzy systems in FM model

2021 ◽  
Vol 297 ◽  
pp. 01035
Author(s):  
Rachid Naoual ◽  
Abderrahim El-Amrani ◽  
Ismail Boumhidi
Keyword(s):  
Model Reduction ◽  
State Space ◽  
Linear Matrix Inequalities ◽  
Fuzzy Systems ◽  
Linear Matrix ◽  
Two Dimensional ◽  
Matrix Inequalities ◽  
Finite Frequency ◽  
Frequency Model ◽  
Takagi Sugeno

This paper deals with the problem of H∞ model reduction for two-dimensional (2D) discrete Takagi-Sugeno (T-S) fuzzy systems described by Fornasini-Marchesini local state-space (FM LSS) models, over finite frequency (FF) domain. New design conditions guaranteeing the FF H∞ model reduction are established in terms of Linear Matrix Inequalities (LMIs). To highlight the effectiveness of the proposed H∞ model reduction design, a numerical example is given.

Observer-based exponential stabilization of Takagi–Sugeno fuzzy systems with state and input delays

2011 ◽  
Vol 225 (7) ◽  
pp. 993-1004 ◽  
Author(s):  
C-S Chiu ◽  
T-S Chiang
Keyword(s):  
Time Delay ◽  
Output Feedback ◽  
Fuzzy Systems ◽  
Control Method ◽  
Exponential Stabilization ◽  
Delay Systems ◽  
Discrete Time Delay ◽  
State And Input Delays ◽  
Input Delays ◽  
Takagi Sugeno

This paper proposes an exponential stabilization control method for uncertain Takagi–Sugeno fuzzy systems with state and input delays via output feedback. First, a unified memoryless fuzzy observer-based control method is introduced for stabilizing continuous and discrete uncertain time-delay fuzzy systems. Then, the exponential stability conditions are derived and converted to solving linear matrix inequality (LMI) problems. Based on the developed novel LMI algorithms, the controller and observer gains are able to be separately designed even in the presence of modelling uncertainty, state delay, and input delay. In comparison with existing techniques the proposed technique produces controlled states and state estimation errors that are guaranteed to exponentially converge to zero via output feedback. This is a major breakthrough for the control of uncertain systems with both state and input unavailable time-varying delays. Finally, two studies are carried out on continuous and discrete time-delay systems. Numerical simulation and comparison results demonstrate the quality of the obtained performance.

scholarly journals Pinning Stabilization of Complex Networks Coupled with Time Delay and Disturbed with Stochastic Noise

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Chun-Xia Fan ◽  
Yu Gu ◽  
Qingyang Wei
Keyword(s):  
Time Delay ◽  
Complex Networks ◽  
Equilibrium Point ◽  
Complex Network ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Stochastic Noise ◽  
Matrix Inequalities ◽  
Stabilization Problem ◽  
Control Criteria

A pinning stabilization problem of complex networks with time-delay coupling is studied under stochastic noisy circumstances in this paper. Only one controller is used to stabilize the network to the equilibrium point when the network is connected and the minimal number of controllers is used when the network is unconnected, where the structure of complex network is fully used. Some criteria are achieved to control the complex network under stochastic noise in the form of linear matrix inequalities. Several examples are given to show the validity of the proposed control criteria.

A new control approach for a class of linear switched systems with time-varying delay

2021 ◽  
pp. 014233122199272
Author(s):  
Abbas Zabihi Zonouz ◽  
Mohammad Ali Badamchizadeh ◽  
Amir Rikhtehgar Ghiasi
Keyword(s):  
Stability Analysis ◽  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Switching Systems ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Time Varying Delay ◽  
Linear Switching Systems ◽  
The Stability ◽  
Varying Delay

In this paper, a new method for designing controller for linear switching systems with varying delay is presented concerning the Hurwitz-Convex combination. For stability analysis the Lyapunov-Krasovskii function is used. The stability analysis results are given based on the linear matrix inequalities (LMIs), and it is possible to obtain upper delay bound that guarantees the stability of system by solving the linear matrix inequalities. Compared with the other methods, the proposed controller can be used to get a less conservative criterion and ensures the stability of linear switching systems with time-varying delay in which delay has way larger upper bound in comparison with the delay bounds that are considered in other methods. Numerical examples are given to demonstrate the effectiveness of proposed method.

scholarly journals A New Stability Criterion for Systems with Distributed Time-Varying Delays via Mixed Inequalities Method

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Jun-kang Tian ◽  
Yan-min Liu
Keyword(s):  
Linear Matrix Inequalities ◽  
Stability Criterion ◽  
Linear Matrix ◽  
Time Varying ◽  
Matrix Inequalities ◽  
Numerical Examples ◽  
Delay Dependent ◽  
Delay Dependent Stability ◽  
New Inequalities

This paper is concerned with the delay-dependent stability of systems with distributed time-varying delays. The novelty relies on the use of some new inequalities which are less conservative than some existing inequalities. A less conservative stability criterion is obtained by constructing some new augmented Lyapunov–Krasovskii functionals, which are given in terms of linear matrix inequalities. The effectiveness of the presented criterion is demonstrated by two numerical examples.

Non-Fragile Decentralized Control for the Uncertain Singular Large-Scale Systems with Time-Delay

2011 ◽  
Vol 317-319 ◽  
pp. 2204-2207
Author(s):  
Dong Mei Yang ◽  
Qing Sun
Keyword(s):  
Time Delay ◽  
Linear Matrix Inequalities ◽  
Decentralized Control ◽  
Large Scale ◽  
Controller Design ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Large Scale Systems ◽  
System With Time Delay

This paper is concerned with the non-fragile decentralized controller design problem for uncertain singular large-scale system with time-delay. Sufficient condition for the controller is expressed in terms of linear matrix inequalities(LMIs). When this condition is feasible, the desired controller can be obtained with additive gain perturbations and multiplicative gain perturbations. Finally, a numerical example is also given to illustrate the effectiveness.

The Optimal Regulations of the Interconnection-Degrees of Large Scale Systems under Instable Case

2012 ◽  
Vol 235 ◽  
pp. 107-110
Author(s):  
Ying Ge Wo
Keyword(s):  
Cost Function ◽  
Linear Matrix Inequalities ◽  
Large Scale ◽  
Large System ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Stabilization Problem ◽  
Large Scale Systems ◽  
The Cost

This paper discusses the stabilization problem of a large-scale system via cutting off the connections or decreasing the degree of interconnections among its subsystems subject to a cost function. Under the assumption that the large system is unstable but its sub-systems are all stable, a sufficient condition about the degree of interconnection is presented via cutting off the connections or decreasing the degree of interconnections among its subsystems such that the new large system is stable. This condition can be expressed by linear matrix inequalities (LMIs). Based on this analysis, an optimal regulation for such controls is obtained ensures the minimization of the cost function. An illustrating example is also given to show the effectiveness of the proposed method.

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