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Published in: Neural Computing and Applications 10/2019

28-03-2018 | Original Article

A novel robust \(H_{\infty }\) fuzzy state feedback plus state-derivative feedback controller design for nonlinear time-varying delay systems

Authors: S. Ruangsang, W. Assawinchaichote

Published in: Neural Computing and Applications | Issue 10/2019

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Abstract

This paper investigates the problem of designing a robust \(H_{\infty }\) state feedback plus state-derivative feedback control mechanism for a class of uncertain nonlinear time-varying delay systems described by a Takagi–Sugeno fuzzy model. A linear matrix inequality approach is applied to derive a robust controller for such a system. The proposed controller satisfies design requirements that ensure that the closed-loop system is asymptotically stable and meets pre-prescribed \(H_{\infty }\) performance index values. Finally, the illustrative examples are simulated to illustrate the effectiveness of the proposed methodology.

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Appendix
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Literature
1.
go back to reference Assawinchaichote W (2014) Further results on robust fuzzy dynamic systems with \(D\)-stability constraints, Internat. J Appl Math Comput Sci 24:785–794 Assawinchaichote W (2014) Further results on robust fuzzy dynamic systems with \(D\)-stability constraints, Internat. J Appl Math Comput Sci 24:785–794
2.
go back to reference Nguang SK, Shi P (2000) Stabilisation of a class of nonlinear time-delay systems using fuzzy models. In: Proceedings of IEEE conference on decision and control, pp 4415–4419 Nguang SK, Shi P (2000) Stabilisation of a class of nonlinear time-delay systems using fuzzy models. In: Proceedings of IEEE conference on decision and control, pp 4415–4419
3.
go back to reference Wang WJ, Lin WW (2000) State feedback stabilization for T–S fuzzy time delay systems. In: Proceedings of IEEE conference on fuzzy systems, pp 561–565 Wang WJ, Lin WW (2000) State feedback stabilization for T–S fuzzy time delay systems. In: Proceedings of IEEE conference on fuzzy systems, pp 561–565
4.
go back to reference Yoneyama J (2000) Robust control analysis and synthesis for uncertain fuzzy systems with time-delay. In: Proceedings of IEEE conference on fuzzy systems, pp 396–401 Yoneyama J (2000) Robust control analysis and synthesis for uncertain fuzzy systems with time-delay. In: Proceedings of IEEE conference on fuzzy systems, pp 396–401
5.
go back to reference Lee KR, Kim JH, Jeung ET, Park HB (2000) Output feedback robust: \(H_{\infty }\) control of uncertain fuzzy dynamic systems with time-varying delay. IEEE Trans Fuzzy Syst 8:657–664 Lee KR, Kim JH, Jeung ET, Park HB (2000) Output feedback robust: \(H_{\infty }\) control of uncertain fuzzy dynamic systems with time-varying delay. IEEE Trans Fuzzy Syst 8:657–664
6.
go back to reference Wang RJ, Lin WW, Wang WJ (2004) Stabilizability of linear quadratic state feedback for uncertain fuzzy time-delay systems. IEEE Trans Syst Man Cybern Part B 34:1–4CrossRef Wang RJ, Lin WW, Wang WJ (2004) Stabilizability of linear quadratic state feedback for uncertain fuzzy time-delay systems. IEEE Trans Syst Man Cybern Part B 34:1–4CrossRef
7.
go back to reference Cao YY, Frank PM (2001) Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi–Sugeno fuzzy models. Fuzzy Sets Syst 124:213–229MathSciNetCrossRef Cao YY, Frank PM (2001) Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi–Sugeno fuzzy models. Fuzzy Sets Syst 124:213–229MathSciNetCrossRef
8.
go back to reference Assawinchaichote W (2014) A new robust \(H_{\infty }\) fuzzy state-feedback control design for nonlinear Markovianjump systems with time-varying delay. Control Cybern 43:227–248 Assawinchaichote W (2014) A new robust \(H_{\infty }\) fuzzy state-feedback control design for nonlinear Markovianjump systems with time-varying delay. Control Cybern 43:227–248
9.
go back to reference Hill DJ, Moylan PJ (1980) Dissipative dynamical systems: basic input-output and state properties. J Frankl Inst 309:327–357MathSciNetCrossRef Hill DJ, Moylan PJ (1980) Dissipative dynamical systems: basic input-output and state properties. J Frankl Inst 309:327–357MathSciNetCrossRef
10.
go back to reference Ball JA, Helton JW (1989) \(H_{\infty }\) control for nonlinear plants: connection with differential games. In: IEEE conference on decision and control, pp 956–962 Ball JA, Helton JW (1989) \(H_{\infty }\) control for nonlinear plants: connection with differential games. In: IEEE conference on decision and control, pp 956–962
11.
go back to reference Isidori A (1991) Feedback control of nonlinear systems. In: Proceedings of first European control conference, pp 1001–1012 (1991) Isidori A (1991) Feedback control of nonlinear systems. In: Proceedings of first European control conference, pp 1001–1012 (1991)
12.
go back to reference van der Schaft AJ (1992) \(L_2\)-gain analysis of nonlinear systems and nonlinear state feedback \(H_{\infty }\) control. IEEE Trans Autom Control 37:770–784 van der Schaft AJ (1992) \(L_2\)-gain analysis of nonlinear systems and nonlinear state feedback \(H_{\infty }\) control. IEEE Trans Autom Control 37:770–784
13.
go back to reference Isidori A, Astofi A (1992) Disturbance attenuation and \(H_{\infty }\)-control via measurement feedback in nonlinear systems. IEEE Trans Autom Control 37:1283–1293 Isidori A, Astofi A (1992) Disturbance attenuation and \(H_{\infty }\)-control via measurement feedback in nonlinear systems. IEEE Trans Autom Control 37:1283–1293
14.
go back to reference van der Schaft AJ (1991) A state-space approach to nonlinear \(H_{\infty }\) control. Syst Control Lett 16:1–8 van der Schaft AJ (1991) A state-space approach to nonlinear \(H_{\infty }\) control. Syst Control Lett 16:1–8
15.
go back to reference Choi HH, Chung MJ (1995) Memoryless \(H_{\infty }\) controller design for linear systems with delayed state and control. Autom J IFAC 31:917–919 Choi HH, Chung MJ (1995) Memoryless \(H_{\infty }\) controller design for linear systems with delayed state and control. Autom J IFAC 31:917–919
16.
go back to reference Kim JH, Jeung ET, Park HB (1996) Robust control parameter uncertain delay systems in state and control input. Autom J IFAC 32:1337–1339MathSciNetCrossRef Kim JH, Jeung ET, Park HB (1996) Robust control parameter uncertain delay systems in state and control input. Autom J IFAC 32:1337–1339MathSciNetCrossRef
17.
go back to reference Jeung ET, Kim JH, Park HB (1998) \(H_{\infty }\) output feedback controller design for linear systems with time-varying delayed state. IEEE Trans Autom Control 43:971–974 Jeung ET, Kim JH, Park HB (1998) \(H_{\infty }\) output feedback controller design for linear systems with time-varying delayed state. IEEE Trans Autom Control 43:971–974
18.
go back to reference Mahmoud MS, AI-Muthairi NF (1994) Design of robust controllers for time delay systems. IEEE Trans Autom Control 39:995–999MathSciNetCrossRef Mahmoud MS, AI-Muthairi NF (1994) Design of robust controllers for time delay systems. IEEE Trans Autom Control 39:995–999MathSciNetCrossRef
19.
go back to reference Tanaka K, Ikeda T, Wang HO (1996) Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stability, \(H_{\infty }\) control theory, and linear matrix inequality. IEEE Trans Fuzzy Syst 4:1–13 Tanaka K, Ikeda T, Wang HO (1996) Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stability, \(H_{\infty }\) control theory, and linear matrix inequality. IEEE Trans Fuzzy Syst 4:1–13
20.
go back to reference Chen BS, Tseng CS, He YY (2000) Mixed \(H_{2}\)/\(H_{\infty }\) fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach. IEEE Trans Fuzzy Syst 8:249–265 Chen BS, Tseng CS, He YY (2000) Mixed \(H_{2}\)/\(H_{\infty }\) fuzzy output feedback control design for nonlinear dynamic systems: an LMI approach. IEEE Trans Fuzzy Syst 8:249–265
21.
go back to reference Cirovic G, Pamucar D (2013) Decision support model for prioritizing railway level crossings for safety improvements: application of the adaptive neuro-fuzzy system. Expert Syst Appl 40(6):2208–2223CrossRef Cirovic G, Pamucar D (2013) Decision support model for prioritizing railway level crossings for safety improvements: application of the adaptive neuro-fuzzy system. Expert Syst Appl 40(6):2208–2223CrossRef
22.
go back to reference Cirovic G, Pamucar D, Bozanic D (2014) Green logistic vehicle routing problem: routing light delivery vehicles in urban areas using a neuro-fuzzy model. Expert Syst Appl 41(9):4245–4258CrossRef Cirovic G, Pamucar D, Bozanic D (2014) Green logistic vehicle routing problem: routing light delivery vehicles in urban areas using a neuro-fuzzy model. Expert Syst Appl 41(9):4245–4258CrossRef
23.
go back to reference Pamucar D, Ljubojevic S, Kostadinovic D, Dorovic B (2016) Cost and risk aggregation in multi-objective route planning for hazardous materials transportation—a neuro-fuzzy and artificial bee colony approach. Expert Syst Appl 65:1–15CrossRef Pamucar D, Ljubojevic S, Kostadinovic D, Dorovic B (2016) Cost and risk aggregation in multi-objective route planning for hazardous materials transportation—a neuro-fuzzy and artificial bee colony approach. Expert Syst Appl 65:1–15CrossRef
24.
go back to reference Pamucar D, Lukovac V, Pejcic-Tarle S (2013) Application of adaptive neuro fuzzy inference system in the process transportation support. Asia-Pac J Oper Res 30(2):1–32CrossRef Pamucar D, Lukovac V, Pejcic-Tarle S (2013) Application of adaptive neuro fuzzy inference system in the process transportation support. Asia-Pac J Oper Res 30(2):1–32CrossRef
25.
go back to reference Pamucar D, Vasin L, Atanaskovic P, Milicic M (2016) Planning the city logistics terminal location by applying the green \(p\)-median model and type-2 neurofuzzy network. Comput Intell Neurosci 6972818:1–15 Pamucar D, Vasin L, Atanaskovic P, Milicic M (2016) Planning the city logistics terminal location by applying the green \(p\)-median model and type-2 neurofuzzy network. Comput Intell Neurosci 6972818:1–15
26.
go back to reference Pamucar D, Bozanic D, Milic A (2016) Selection of a course of action by obstacle employment group based on a fuzzy logic system. Yugoslav J Oper Res 26(1):75–90MathSciNetCrossRef Pamucar D, Bozanic D, Milic A (2016) Selection of a course of action by obstacle employment group based on a fuzzy logic system. Yugoslav J Oper Res 26(1):75–90MathSciNetCrossRef
27.
go back to reference Pamucar D, Bozanic D, Komazec N (2016) Risk assessment of natural disasters using fuzzy logic system of type 2. Management 80:23–32 Pamucar D, Bozanic D, Komazec N (2016) Risk assessment of natural disasters using fuzzy logic system of type 2. Management 80:23–32
28.
go back to reference Hsiao FH (2012) An NN-based approach to \(H_{\infty }\) fuzzy control for nonlinear multiple time delay systems by dithers. Int J Fuzzy Syst 14:474–489 Hsiao FH (2012) An NN-based approach to \(H_{\infty }\) fuzzy control for nonlinear multiple time delay systems by dithers. Int J Fuzzy Syst 14:474–489
29.
go back to reference Idrissi S, Tissir EH, Boumhidi I, Chaibi N (2014) Robust \(H_{\infty }\) control for uncertain T-S fuzzy systems via delay partitioning approach. Int J Ecol Dev 28:96–108 Idrissi S, Tissir EH, Boumhidi I, Chaibi N (2014) Robust \(H_{\infty }\) control for uncertain T-S fuzzy systems via delay partitioning approach. Int J Ecol Dev 28:96–108
30.
go back to reference Wang YL, Han QL (2014) Modelling and observer-based \(H_{\infty }\) controller design for networked control systems. IET Control Theory Appl 8:1478–1486 Wang YL, Han QL (2014) Modelling and observer-based \(H_{\infty }\) controller design for networked control systems. IET Control Theory Appl 8:1478–1486
31.
go back to reference Peng C, Yue D, Tian YC (2009) New approach on robust delay dependent \(H_{\infty }\) control for uncertain T–S fuzzy systems with interval time varying delay. IEEE Trans Fuzzy Syst 17:890–900 Peng C, Yue D, Tian YC (2009) New approach on robust delay dependent \(H_{\infty }\) control for uncertain T–S fuzzy systems with interval time varying delay. IEEE Trans Fuzzy Syst 17:890–900
32.
go back to reference Ma Y, Yan H (2013) Delay dependent filter for T–S fuzzy time delay systems with exponential stability. Adv Differ Equ 2013:362–378MathSciNetCrossRef Ma Y, Yan H (2013) Delay dependent filter for T–S fuzzy time delay systems with exponential stability. Adv Differ Equ 2013:362–378MathSciNetCrossRef
33.
go back to reference Qing G, He H, Guang F, Lu L, Yong W (2013) Robust \(H_{\infty }\) stabilization of uncertain T-S fuzzy Systems via dynamic integral sliding mode control. Intell Control Autom Sci 3:485–490 Qing G, He H, Guang F, Lu L, Yong W (2013) Robust \(H_{\infty }\) stabilization of uncertain T-S fuzzy Systems via dynamic integral sliding mode control. Intell Control Autom Sci 3:485–490
34.
go back to reference Gao Q, Feng G, Xi Z, Qiu J (2014) A new design of robust \(H_{\infty }\) sliding mode control for uncertain stochastic T–S fuzzy time delay systems. IEEE Trans Cybern 44:1556–1566 Gao Q, Feng G, Xi Z, Qiu J (2014) A new design of robust \(H_{\infty }\) sliding mode control for uncertain stochastic T–S fuzzy time delay systems. IEEE Trans Cybern 44:1556–1566
35.
go back to reference Assawinchaichote W, Nguang SK, Shi P, Boukas EK (2008) \(H_{\infty }\) Fuzzy state feedback control design for nonlinear systems with \(D\)-stability constraints: an LMI approach. Int J Math Comput Simul 78:514–531 Assawinchaichote W, Nguang SK, Shi P, Boukas EK (2008) \(H_{\infty }\) Fuzzy state feedback control design for nonlinear systems with \(D\)-stability constraints: an LMI approach. Int J Math Comput Simul 78:514–531
36.
go back to reference Assawinchaichote W (2012) A non-fragile \(H_{\infty }\) output feedback controller for uncertain fuzzy dynamical systems with multiple time-scales. Int J Comput Commun Control 7:8–19 Assawinchaichote W (2012) A non-fragile \(H_{\infty }\) output feedback controller for uncertain fuzzy dynamical systems with multiple time-scales. Int J Comput Commun Control 7:8–19
37.
go back to reference Shi P, Su X, Li F (2016) Dissipativity-based filtering for fuzzy switched systems with stochastic perturbation. IEEE Trans Autom Control 61(6):1694–1699MathSciNetCrossRef Shi P, Su X, Li F (2016) Dissipativity-based filtering for fuzzy switched systems with stochastic perturbation. IEEE Trans Autom Control 61(6):1694–1699MathSciNetCrossRef
38.
go back to reference Tao J, Su H, Shi P, Lu R, Wu Z (2017) Dissipativity-based reliable control for fuzzy Markov jump systems with actuator faults. IEEE Trans Cybern 47(9):2377–2388CrossRef Tao J, Su H, Shi P, Lu R, Wu Z (2017) Dissipativity-based reliable control for fuzzy Markov jump systems with actuator faults. IEEE Trans Cybern 47(9):2377–2388CrossRef
39.
go back to reference Wu Z, Dong S, Shi P, Su H, Huang T, Lu R (2017) Fuzzy-model-based non fragile guaranteed cost control of nonlinear Markov jump systems. IEEE Trans Syst Man Cybern Syst 47(8):2388–2397CrossRef Wu Z, Dong S, Shi P, Su H, Huang T, Lu R (2017) Fuzzy-model-based non fragile guaranteed cost control of nonlinear Markov jump systems. IEEE Trans Syst Man Cybern Syst 47(8):2388–2397CrossRef
40.
go back to reference Dong S, Wu Z, Shi P, Su H, Lu R (2017) Reliable control of fuzzy systems with quantization and switched actuator failures. IEEE Trans Syst Man Cybern Syst 47(8):2198–2208CrossRef Dong S, Wu Z, Shi P, Su H, Lu R (2017) Reliable control of fuzzy systems with quantization and switched actuator failures. IEEE Trans Syst Man Cybern Syst 47(8):2198–2208CrossRef
41.
go back to reference Wang H, Liu X, Shi P (2017) Observer-based fuzzy adaptive output-feedback control of stochastic nonlinear multiple time-delay systems. IEEE Trans Cybern 47(9):2568–2578CrossRef Wang H, Liu X, Shi P (2017) Observer-based fuzzy adaptive output-feedback control of stochastic nonlinear multiple time-delay systems. IEEE Trans Cybern 47(9):2568–2578CrossRef
42.
go back to reference Reithmeier E, Leitmann G (2003) Robust vibration control of dynamical systems based on the derivative of the state. Arch Appl Mech 72(12):856–864MATH Reithmeier E, Leitmann G (2003) Robust vibration control of dynamical systems based on the derivative of the state. Arch Appl Mech 72(12):856–864MATH
44.
go back to reference Araujo J, Dorea C, Gonalves L, Datta B (2016) State derivative feedback in second-order linear systems: a comparative analysis of perturbed eigenvalues under coefficient variation. Mech Syst Signal Process 76–77:33–46CrossRef Araujo J, Dorea C, Gonalves L, Datta B (2016) State derivative feedback in second-order linear systems: a comparative analysis of perturbed eigenvalues under coefficient variation. Mech Syst Signal Process 76–77:33–46CrossRef
45.
go back to reference Bhasin S, Kamalapurkar R, Dinh H, Dixon W (2013) Robust identification based state derivative estimation for nonlinear systems. IEEE Trans Autom Control 58(1):187–192MathSciNetCrossRef Bhasin S, Kamalapurkar R, Dinh H, Dixon W (2013) Robust identification based state derivative estimation for nonlinear systems. IEEE Trans Autom Control 58(1):187–192MathSciNetCrossRef
46.
go back to reference Krewpraek N, Assawinchaichote W (2016) \(H_{\infty }\) fuzzy state-feedback control plus state-derivative feedback control synthesis for the photovoltaic system. Asian J Control 18:1441–1452 Krewpraek N, Assawinchaichote W (2016) \(H_{\infty }\) fuzzy state-feedback control plus state-derivative feedback control synthesis for the photovoltaic system. Asian J Control 18:1441–1452
47.
go back to reference Assawinchaichote W (2015) LMIs approach based robust \(H_{\infty }\) fuzzy controller design for nonlinear time varying delay system. In: Applications and developments control theory: perspectives. Nova Science Publishers, New York Assawinchaichote W (2015) LMIs approach based robust \(H_{\infty }\) fuzzy controller design for nonlinear time varying delay system. In: Applications and developments control theory: perspectives. Nova Science Publishers, New York
Metadata
Title
A novel robust fuzzy state feedback plus state-derivative feedback controller design for nonlinear time-varying delay systems
Authors
S. Ruangsang
W. Assawinchaichote
Publication date
28-03-2018
Publisher
Springer London
Published in
Neural Computing and Applications / Issue 10/2019
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-018-3452-y

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