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## Feedback Linearization for Input-saturation Nonlinear System Based on T-S Fuzzy Model

### Citations

1572 |
Fuzzy identification of systems and its application to modeling and control.
- Takagi, Sugeno
- 1985
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Citation Context ...e placement and nonlinearssystem. The i-th IF-THEN rule of the T-S fuzzy model forsa nonlinear system issRule i : If 1( )w t is 1iFsand and ( )gw t is igF , thens( ) ( ) ( )i ix t A x t B u t= + ,s=-=(1)-=- where, 1,2,...,i L= , n n iA R ×∈ ,sn m iB R ×∈ , L is the numbersof rules, and 1 2( ), ( ),..., ( )gw t w t w t are premise variables.sThe overall fuzzy system iss{ } 1 1 ( ( )) ( ) ( ) ( ) ( ( )) L... |

169 |
Nonlinear control systems. 3rd ed.
- Isidori
- 1995
(Show Context)
Citation Context ... t A x t B u t= + , for 1,2,...,i L=sands( ) ( )iz t T x t=s(6) for 1,2,...,i L= .sBy substitute state x(t) of (6) into (1), the linear model ofsi-th rule can bes( ) ( ) ( )ci ciZ t A Z t B u t= + s=-=(7)-=- where, 1ci i i iA T AT − = , ci i iB T B= . The overall fuzzyscoordinate changed state iss1 ( ) ( ( )) ( ) L i i i Z t h w t T x t = = ∑s(8) which is considered as the summation of the statessx(t) th... |

153 |
H ∞ design with pole placement constrains: an LMI approach
- Chilali, Gahinet
- 1996
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Citation Context ...KZ t u KZ t S t u KZ t u u KZ t u KZ t > = − < < − < −s(18) Defines{ }DZtSd ∈∀= ),(min0s(19) where, D is a compact space and let a matrix 0Ssissconsisted by element 0dsor 1. Setsv(t)=KZ(t),s=-=(20)-=- 3.1 Corollary 1 System (16) is D-stable if and only if there exists assymmetric matrix X>0 such that .0 )( )( 0 0 < −++ ++− rXKSBAXqX XKSBAqXrX T cncn cncns(21) where, q is the pole placement... |

117 |
The Control Handbook
- Levine
- 1996
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Citation Context ...=∑sfrom (4). The result can be represented in the followingstheorem: 2.1.1 Theorem 1sUnder the assumption 1, ifs1 1 1 1 ( ) ( ) l l L m L n i cin k k i in j j i k i j h b u t h a z t = = = = = −∑∑ ∑∑s=-=(15)-=- for each lnshas the solution for ( )ku t , then (9) can be thesform ofs( ) ( ) ( )cn cnZ t A Z t B v t= + s(16) where, 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0... |

30 |
Parallel Distributed Compensation of Nonlinear Systems by Takagi-Sugeno Fuzzy Model
- Wang, O, et al.
- 1995
(Show Context)
Citation Context ...he numbersof rules, and 1 2( ), ( ),..., ( )gw t w t w t are premise variables.sThe overall fuzzy system iss{ } 1 1 ( ( )) ( ) ( ) ( ) ( ( )) L i i i i L i i w t A x t B u t x t w t = = + = ∑ ∑ µ µs=-=(2)-=- where, 1 2( ) ( ), ( ),..., ( )gw t w t w t w t = . Let Won-IL Seo, Seung-Mi Moon, Sook-Youn Kwon, Jin-Hee Park and Jae-Hyun Lim Vol 8 (S1) : January 2015 : www.indjst.org Indian Journal of Sc... |

28 |
Fuzzy modeling and control of multilayer incinerator. Fuzzy Sets Syst
- Sugeno, GT
- 1986
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Citation Context ...t = = ∑ µ µ , nonlinear system can be describedsas { } 1 ( ) ( ( )) ( ) ( ) L i i i i x t h w t A x t B u t = = +∑ .s(3) Membership function ( ( ))ih w tsshould satisfy: 1 ( ( )) 1. L i i h w t = =∑s=-=(4)-=- The following assumption is required for the finalsmodel calculation in this paper: 2.1 Assumption 1sIf all T-S fuzzy n-dimension linear models are controllable,sthe following condition should be sat... |

4 |
Controllers for linear systems with bounded actuators: Slab scheduling and anti-windup. Automatica 2013
- Sajjadi, Jabbari
(Show Context)
Citation Context ... model (9) linear. Under the assumption 1, iTsissobtained by following steps: Structure a matrix M as 2 1 1 1 1 1 2 2 2 2 1 2 [ ] i i i i i i i i i i i i i i i M b Ab A b A b b Ab A b A b = µ µs=-=(10)-=- where, ijb is the elements of 1 2[ ... ]i i i imB b b b=sin (1).sFor searching iM , start from 1ibsand end at rank(M)=n.sIf 1i ikA b +µsmakes vectors before this vector and this vectorsrelative, then... |

4 |
Anti-windup for marginally stable plants and its application to open water channel control systems. Control Engineering Practice
- Zaccarian, Li, et al.
(Show Context)
Citation Context ... 1 1 1 ( ) ( ) l l L m L n i cin k k i in j j i k i j h b u t h a z t = = = = = −∑∑ ∑∑s(15) for each lnshas the solution for ( )ku t , then (9) can be thesform ofs( ) ( ) ( )cn cnZ t A Z t B v t= + s=-=(16)-=- where, 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 cnA = ... |

3 |
Designing Override and Feedforward Controls
- BUCKLEY
- 1971
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Citation Context ...fore this vector and this vectorsrelative, then delete this vector and start with ( 1)i kb + . Thesinverse of M is 1 11 12 1 1 21 22 2 2 T T T i i i i TT T T i i i M e e e e e e − = µ µ .s=-=(11)-=- For the multiple-input case, iTsis obtained as follows: 1 1 1 1 1 1 1 1 2 1 2 2 2 2 2 2 [( ) ( ) ( ) ( ) ( ) ( ) ] T T T i i i i i i T T T i i i i i T e e A e A e e A e A − − = µ µ µ µ µ µ µ µs... |

3 |
Antiwindup synthesis for nonlinear dynamic inversion control schemes
- Herrmann, Menon, et al.
- 2010
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Citation Context ...ering of this, an anti-windup controller is needed.sConsider the saturation input lim lim lim lim lim lim , ( ) ( ) ( ( )) ( ) ( ) , ( ) u u t u v t sat u t u t u u t u u u t u ≥ = = − < < − ≤ −s=-=(17)-=- u(t) is input before saturation segment and lim 0u >sissinput limitation. Degree of feedback saturation is definedsas: Won-IL Seo, Seung-Mi Moon, Sook-Youn Kwon, Jin-Hee Park and Jae-Hyun Lim Vol 8 (... |

2 |
On the linear equivalents of nonlinear systems. Syst Contr Lett
- Su
- 1982
(Show Context)
Citation Context ...ange, the i-th rule of thesfuzzy model for the nonlinear system is Rule i: If 1( )w t is 1iFsand and ( )gw t is igF , thens( ) ( ) ( )i ix t A x t B u t= + , for 1,2,...,i L=sands( ) ( )iz t T x t=s=-=(6)-=- for 1,2,...,i L= .sBy substitute state x(t) of (6) into (1), the linear model ofsi-th rule can bes( ) ( ) ( )ci ciZ t A Z t B u t= + s(7) where, 1ci i i iA T AT − = , ci i iB T B= . The overall fuzz... |

1 |
Asymptotic and robust stability of T-S fuzzy genetic regulatory networks with time-varying delays
- Liu, Yue
(Show Context)
Citation Context ...Journal of Science and Technology 99s1 ( ( )) ( ( )) ( ( )) i i L i i w t h w t w t = = ∑ µ µ , nonlinear system can be describedsas { } 1 ( ) ( ( )) ( ) ( ) L i i i i x t h w t A x t B u t = = +∑ .s=-=(3)-=- Membership function ( ( ))ih w tsshould satisfy: 1 ( ( )) 1. L i i h w t = =∑s(4) The following assumption is required for the finalsmodel calculation in this paper: 2.1 Assumption 1sIf all T-S fuzzy... |

1 |
Sugeno M. Stability analysis and design of fuzzy control systems. Fuzzy Sets Syst
- Tanka
- 1992
(Show Context)
Citation Context ...model calculation in this paper: 2.1 Assumption 1sIf all T-S fuzzy n-dimension linear models are controllable,sthe following condition should be satisfied: 1... ni i i i irank B A B A B n − = .s=-=(5)-=- To deal with the coordinate change, the i-th rule of thesfuzzy model for the nonlinear system is Rule i: If 1( )w t is 1iFsand and ( )gw t is igF , thens( ) ( ) ( )i ix t A x t B u t= + , for 1,2,.... |

1 |
Xing G.-Q Discrete-time LQ optimal control of satellite formations in elliptical orbits based on feedback linearization
- Li, Liu
(Show Context)
Citation Context ...l ofsi-th rule can bes( ) ( ) ( )ci ciZ t A Z t B u t= + s(7) where, 1ci i i iA T AT − = , ci i iB T B= . The overall fuzzyscoordinate changed state iss1 ( ) ( ( )) ( ) L i i i Z t h w t T x t = = ∑s=-=(8)-=- which is considered as the summation of the statessx(t) through transformation iTswith the proportion ofsmembership ih . The overall fuzzy system is { } 1 ( ) ( ( )) ( ) ( ) L i ci ci i Z t h w t A Z... |

1 |
Linearized large signal modeling, analysis, and control design of phasecontrolled series-parallel resonant converters using state feedback
- Aboushady, Ahmed, et al.
(Show Context)
Citation Context ...d as the summation of the statessx(t) through transformation iTswith the proportion ofsmembership ih . The overall fuzzy system is { } 1 ( ) ( ( )) ( ) ( ) L i ci ci i Z t h w t A Z t B u t = = +∑ . =-=(9)-=- Now problem is to derive iTsand u(t) which make thesT-S fuzzy model (9) linear. Under the assumption 1, iTsissobtained by following steps: Structure a matrix M as 2 1 1 1 1 1 2 2 2 2 1 2 [ ] i i i i ... |

1 |
Kinnaert M, Luyben W. Conditioning technique, a general anti-windup and bumpless transfer method. Automatica.1987
- Hanus
(Show Context)
Citation Context ... For the multiple-input case, iTsis obtained as follows: 1 1 1 1 1 1 1 1 2 1 2 2 2 2 2 2 [( ) ( ) ( ) ( ) ( ) ( ) ] T T T i i i i i i T T T i i i i i T e e A e A e e A e A − − = µ µ µ µ µ µ µ µs=-=(12)-=- Then the above state transformation iTschanged thesi-th linear system of fuzzy system into the controllablescanonical forms( ) ( ) ( )ci ciZ t A Z t B u t= + s(13) where, 1 2 3 ( 1) ( 2) ( 3) 0 1 0 ... |

1 |
Prodromos D. Observer-based anti-windup scheme for non-linear systems with input constraints
- Navneet
- 1999
(Show Context)
Citation Context ... A e A − − = µ µ µ µ µ µ µ µs(12) Then the above state transformation iTschanged thesi-th linear system of fuzzy system into the controllablescanonical forms( ) ( ) ( )ci ciZ t A Z t B u t= + s=-=(13)-=- where, 1 2 3 ( 1) ( 2) ( 3) 0 1 0 0 0 0 0 ... 0 0 0 1 0 0 0 0 ... 0 ... 0 0 0 1 0 0 0 ... 0 ... 0 1 0 00 0 0 ... 0 0 0 1 00 0 0 ... 0 ... 0 0 0 10 0 0 ... 0 ... l l l l q k k k in in in in n ci in n ... |

1 |
Kothare M, Morari M. Anti-windup design for internal model control
- Zheng
- 1994
(Show Context)
Citation Context ...z t z t z t h b u th a z t − = = = = + + = = = = = + ∑∑ ∑∑ ∑∑∑∑ s=-=(14)-=- where, ( )ku tsis the k-th input and remind that 1 ( ( )) 1 L i i h w t = =∑sfrom (4). The result can be represented in the followingstheorem: 2.1.1 Theorem 1sUnder the assumption 1, ifs1 1 1 1 ( ) (... |

1 |
Linearization of discrete-time T-S fuzzy model with multiple input
- Wang, Park, et al.
(Show Context)
Citation Context ... : January 2015 : www.indjst.org Indian Journal of Science and Technology 101 lim lim lim lim lim lim , ( ) ( ) ( ) 1, ( ) , ( ) ( ) u KZ t u KZ t S t u KZ t u u KZ t u KZ t > = − < < − < −s=-=(18)-=- Defines{ }DZtSd ∈∀= ),(min0s(19) where, D is a compact space and let a matrix 0Ssissconsisted by element 0dsor 1. Setsv(t)=KZ(t),s(20) 3.1 Corollary 1 System (16) is D-stable if and only if there exi... |

1 |
Linearization of T-S fuzzy systems and robust H-infinity control
- Yoon, Wang, et al.
(Show Context)
Citation Context ...Indian Journal of Science and Technology 101 lim lim lim lim lim lim , ( ) ( ) ( ) 1, ( ) , ( ) ( ) u KZ t u KZ t S t u KZ t u u KZ t u KZ t > = − < < − < −s(18) Defines{ }DZtSd ∈∀= ),(min0s=-=(19)-=- where, D is a compact space and let a matrix 0Ssissconsisted by element 0dsor 1. Setsv(t)=KZ(t),s(20) 3.1 Corollary 1 System (16) is D-stable if and only if there exists assymmetric matrix X>0 such t... |

1 |
Azizur R. High-Speed control of IPMSM drives using improved fuzzy logic algorithms
- Nasir
(Show Context)
Citation Context ...ement 0dsor 1. Setsv(t)=KZ(t),s(20) 3.1 Corollary 1 System (16) is D-stable if and only if there exists assymmetric matrix X>0 such that .0 )( )( 0 0 < −++ ++− rXKSBAXqX XKSBAqXrX T cncn cncns=-=(21)-=- where, q is the pole placement disk center and r is radius. The proof is clearly based on the work of20. Equations(21) can be solved by LMI, then v(t) in (20) can besdesigned with anti-windup ability... |