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Non-fragile observer-based passive control for uncertain time delay systems subjected to input nonlinearity. (English) Zbl 1204.34101
A class of uncertain time delay systems subject to an input nonlinearity is considered. For this class of systems, the problem of non-fragile observer-based passive control is investigated by using sliding mode control. First, the authors design an observer for estimating the phase state systems. Then, a sliding surfaces is designed on the state-estimation space. After that, a sufficient condition for asymptotic stability and passivity of the system combined with an error system and sliding mode dynamics is obtained. Furthermore, a novel control law is proposed such that the sliding surface is reached in a finite time in the state-estimation space. Finally, a simulation example is presented to show the validity and advantages of the proposed method.

34K35Functional-differential equations connected with control problems
93C23Systems governed by functional-differential equations
Full Text: DOI
[1] Sun, Yeong-Jeu: Stability criterion for a class of descriptor systems with discrete and distributed time delays, Chaos, solitons & fractals 33, 986-993 (2007) · Zbl 1136.34340 · doi:10.1016/j.chaos.2006.01.067
[2] Lien, Chang-Hua: Delay-dependent and delay-independent guaranteed cost control for uncertain neutral systems with time-varying delays via LMI approach, Chaos, solitons & fractals 33, 1017-1027 (2007) · Zbl 1136.93034 · doi:10.1016/j.chaos.2006.01.066
[3] De La Sen, M.: On positivity of singular regular linear time-delay time-invariant systems subject to multiple internal and external incommensurate point delays, Applied mathematics and computation 190, 382-401 (2007) · Zbl 1117.93034 · doi:10.1016/j.amc.2007.01.053
[4] Lien, Chang-Hua: H$\infty $non-fragile observer-based controls of dynamical systems via LMI optimization approach, Chaos, solitons & fractals 34, 428-436 (2007) · Zbl 1134.93344 · doi:10.1016/j.chaos.2006.03.050
[5] Cui, Bao Tong; Hua, Mingang: Observer-based passive control of linear time-delay systems with parametric uncertainty, Chaos, solitons & fractals 32, 160-167 (2007) · Zbl 1138.93032 · doi:10.1016/j.chaos.2005.10.089
[6] Basili, M.; De Angelis, M.: Optimal passive control of adjacent structures interconnected with nonlinear hysteretic devices, Journal of sound and vibration 301, 106-125 (2007)
[7] Noiray, N.; Durox, D.; Schuller, T.; Candel, S.: Passive control of combustion instabilities involving premixed flames anchored on perforated plates, Proceedings of the combustion institute 31, 1283-1290 (2007)
[8] Chang, Wei-Der: Robust adaptive single neural control for a class of uncertain nonlinear systems with input nonlinearity, Information sciences 171, 261-271 (2005) · Zbl 1068.93029 · doi:10.1016/j.ins.2004.05.001
[9] Fliegner, T.; Logemann, H.; Ryan, E. P.: Low-gain integral control of continuous-time linear systems subject to input and output nonlinearities, Automatica 39, 455-462 (2003) · Zbl 1022.93020 · doi:10.1016/S0005-1098(02)00238-8
[10] Niu, Yugang; Ho, Daniel W. C.: Robust observer design for itô stochastic time-delay systems via sliding mode control, Systems & control letters 55, 781-793 (2006) · Zbl 1100.93047
[11] Tang, Gong-You; Lu, Shan-Shan; Dong, Rui: Optimal sliding mode control for linear time-delay systems with sinusoidal disturbances, Journal of sound and vibration 304, 263-271 (2007) · Zbl 1242.93029
[12] Liu, Leipo; Han, Zhengzhi; Li, Wenlin: Global sliding mode control and application in chaotic systems, Nonlinear dynamics 56, 193-198 (2009) · Zbl 1170.93320 · doi:10.1007/s11071-008-9391-x
[13] Li, Wenlin; Song, Yunzhong: Chaos anti-control of nonlinear system with uncertainties, Acta physica sinica 57, 51-55 (2008) · Zbl 1174.93521
[14] Hsu, Kou-Cheng: Variable structure control design for uncertain dynamic systems with sector nonlinerities, Automatica 34, 505-508 (1998) · Zbl 0949.93013 · doi:10.1016/S0005-1098(97)00233-1
[15] Chiang, Tsung-Ying; Hung, Meei-Ling; Yan, Jun-Juh; Yang, Yi-Sung; Chang, Jen-Fuh: Sliding mode control for uncertain unified chaotic systems with input nonlinearity, Chaos, solitons & fractals 34, 437-442 (2007) · Zbl 1134.93405 · doi:10.1016/j.chaos.2006.03.051
[16] Lin, Jui-Sheng; Yan, Jun-Juh; Liao, Teh-Lu: Chaotic synchronization via adaptive sliding mode observers subject to input nonlinearity, Chaos, solitons & fractals 24, 371-381 (2005) · Zbl 1094.93512 · doi:10.1016/j.chaos.2004.09.042
[17] Yu, Fang-Ming; Chung, Hung-Yuan; Chen, Shi-Yuan: Fuzzy sliding mode controller design for uncertain time-delayed systems with nonlinear input, Fuzzy sets and systems 140, 359-374 (2003) · Zbl 1041.93034 · doi:10.1016/S0165-0114(02)00529-8
[18] Hung, Yung-Ching; Liao, Teh-Lu; Yan, Jun-Juh: Adaptive variable structure control for chaos suppression of unified chaotic systems, Applied mathematics and computation 209, 391-398 (2009) · Zbl 1167.65071 · doi:10.1016/j.amc.2008.12.058
[19] Chiang, Tsung-Ying; Lin, Jui-Sheng; Liao, Teh-Lu; Yan, Jun-Juh: Anti-synchronization of uncertain unified chaotic systems with dead-zone nonlinearity, Nonlinear analysis: theory, methods & applications 68, 2629-2637 (2008) · Zbl 1141.34030 · doi:10.1016/j.na.2007.02.009
[20] Hung, Yung-Ching; Yan, Jun-Juh; Liao, Teh-Lu: Projective synchronization of Chua’s chaotic systems with dead-zone in the control input, Mathematics and computers in simulation 77, 374-382 (2008) · Zbl 1139.65082 · doi:10.1016/j.matcom.2007.03.005
[21] Yau, Her-Terng; Yan, Jun-Juh: Chaos synchronization of different chaotic systems subjected to input nonlinearity, Applied mathematics and computation 197, 775-788 (2008) · Zbl 1135.65409 · doi:10.1016/j.amc.2007.08.014