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On the global convergence of a parameteradjusting LevenbergMarquardt method
Delayrange dependent $H_\infty$ control for uncertain 2Ddelayed systems
1.  College of Sciences, Liaoning Shihua University, Fushun, Liaoning 113001, China, China 
2.  Department of Chemical & Biochemical Engineering, College of Chemistry & Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China 
3.  Department of Chemical and Biomolecular Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China 
References:
[1] 
S. F. Chen, Stability analysis for 2D systems with interval timevarying delays and saturation nonlinearities,, Signal Process, 90 (2010), 2265. Google Scholar 
[2] 
S. F. Chen and I. K. Fong, Delaydependent robust stability and stabilization of twodimensional with statedelayed systems,, Dynamics of Continuous, 16 (2009), 1. Google Scholar 
[3] 
S. F. Chen, Delaydependent stability for 2D systems with timevarying delay subject to state saturation in the Roesser model,, Applied Mathematics and Computation, 216 (2010), 2613. doi: 10.1016/j.amc.2010.03.104. Google Scholar 
[4] 
A. Dhawan and H. Kar, Optimal guaranteed cost control of 2D discrete uncertain systems: An LMI approach,, Signal Processing, 87 (2007), 3075. Google Scholar 
[5] 
A. Dhawan and H. Kar, An LMI approach to robust optimal guaranteed cost control of 2D discrete systems described by the Roesser model,, Signal Processing, 90 (2010), 2648. Google Scholar 
[6] 
A. Dhawan and H. Kar, An improved LMIbased criterion for the design of optimal guaranteed cost controller for 2D discrete uncertain systems,, Signal Processing, 91 (2011), 1032. Google Scholar 
[7] 
A. Dhawa and H. Kar, LMIbased criterion for the robust guaranteed cost control of 2D systems described by the FornasiniMarchesini second model,, Signal Process, 87 (2007), 479. Google Scholar 
[8] 
C. Du, L. Xie and C. Zhang, H_{∞} control and robust stabilization of twodimensional system in Roesser models,, Automatica, 37 (2001), 205. doi: 10.1016/S00051098(00)001552. Google Scholar 
[9] 
C. Du and L. Xie, Stability analysis and stabilization of uncertain twodimensional discrete systems: an LMI approach,, IEEE Trans. Circuits Syst. I Fundam. Theory Appl., 46 (1999), 1371. Google Scholar 
[10] 
Z. X. Duan, Z. R Xiang and H. R Karimi, Delaydependent exponential stabilization of positive 2D switched statedelayed systems in the Roesser model,, Information Sciences, 272 (2014), 173. doi: 10.1016/j.ins.2014.02.121. Google Scholar 
[11] 
L. El Ghaoui, F. Oustry and M. AitRami, A cone complementarity linearization algorithm for static outputfeedback and related problems,, IEEE Transactions on Automatic Control, 42 (1997), 1171. doi: 10.1109/9.618250. Google Scholar 
[12] 
X. P. Guan, Z. Y. Lin and G. R. Duan, Robust guaranteed cost control for 2D discrete systems,, IEE Proc. Control Theory Appl., 148 (2001), 355. Google Scholar 
[13] 
T. Hinamoto, Stability of 2D discrete systems described by the FornasiniMarchesini second model,, IEEE Trans. Circuits Syst. I Fundam. Theory Appl., 44 (1997), 254. doi: 10.1109/81.557373. Google Scholar 
[14] 
T. Kaczorek, TwoDimensional Linear System,, Berlin, (1985). Google Scholar 
[15] 
Y. S. Moon, P. Park, W. H. Kwon and Y. S. Lee, Delaydependent robust stabilization of uncertain statedelayed systems,, International Journal of control, 74 (2001), 1447. doi: 10.1080/00207170110067116. Google Scholar 
[16] 
W. Paszke, K. Galkowski, E. Rogers and D. H. Owens, Hinfinity and guaranteed cost control of discrete linear repetitive processes,, Linear Algebra Appl., 412 (2006), 93. doi: 10.1016/j.laa.2005.01.037. Google Scholar 
[17] 
W. Paszke, J. Lam, K. Galkowski, S. Xu and Z. Lin, Robust stability and stabilisation of 2D discrete statedelayed systems,, Syst. Control Lett., 51 (2004), 278. doi: 10.1016/j.sysconle.2003.09.003. Google Scholar 
[18] 
W. Paszke, J. Lam, K. Galkowski, S. Xu and E. Rogers, H_{∞} control of 2D linear statedelayed systems,, in The 4th IFAC Workshop on TimeDelay Systems (France), (2003), 8. Google Scholar 
[19] 
D. Peng, X. Guan and C. Long, Robust output feedback guaranteed cost control for 2D uncertain state delayed systems,, Asian J. Control, 9 (2004), 470. doi: 10.1111/j.19346093.2007.tb00436.x. Google Scholar 
[20] 
D. Peng and X. Guan, Output feedback H_{∞} control for 2D statedelayed systems,, Circuits Syst. Signal Process, 28 (2009), 147. doi: 10.1007/s0003400890743. Google Scholar 
[21] 
L. M. Wang, S. Y. Mo, D. H. Zhou and F. R. Gao, Robust design of feedback integrated with iterative learning control for batch processes with uncertainties and interval timevarying delays,, J. Process Control, 21 (2011), 987. Google Scholar 
[22] 
L. M. Wang, S. Y. Mo, D. H. Zhou, F. R. Gao and X. Chen, Robust delay dependent iterative learning faulttolerant control for batch processes with state delay and actuator failures,, J. Process Control, 22 (2012), 1273. Google Scholar 
[23] 
L. M. Wang, S. Y. Mo, D. H. Zhou, F. R. Gao and X. Chen, Delayrangedependent robust 2D iterative learning control for batch processes with state delay and uncertainties,, J. Process Control, 23 (2013), 715. Google Scholar 
[24] 
L. M. Wang, X. Chen and F. R. Gao, Delayrangedependent robust BIBO stabilization of 2D discrete delayed systems via LMI approach,, In Proceedings of 19th IFAC World Congress, (2014), 10994. Google Scholar 
[25] 
L. Wu, P. Shi, H. Gao and C. Wang, H_{∞} mode reduction for twodimensional discrete statedelayed systems,, IEE Proc. Vis. Image Signal Process, 156 (2006), 769. Google Scholar 
[26] 
J. M. Xu and L. Yu, Delaydependent guaranteed cost control for uncertain 2D discrete systems with state delay in the FM second model,, Journal of the Franklin Institute, 346 (2009), 159. doi: 10.1016/j.jfranklin.2008.08.003. Google Scholar 
[27] 
J. M. Xu and L. Yu, Delaydependent robust H_{∞} control for uncertain 2D discrete statedelay systems in the second FM model,, Multidimensional Syst. Signal Process, 20 (2009), 333. Google Scholar 
[28] 
S. Ye, W. Wang and Y. Zou, Robust guaranteed cost control for class of twodimensional discrete systems with shiftdelays,, Multidimensional Syst. Signal Process, 20 (2009), 297. doi: 10.1007/s1104500800632. Google Scholar 
[29] 
S. X. Ye, J. Z. Li and J. Yao, Robust H_{∞} control for a class of 2D discrete delayed systems,, ISA Transactions, 53 (2015), 1456. Google Scholar 
[30] 
K. W. Yu and C. H. Lien, Stability criteria for uncertain neutral systems with interval timevarying delays,, Chaos, 38 (2008), 650. doi: 10.1016/j.chaos.2007.01.002. Google Scholar 
show all references
References:
[1] 
S. F. Chen, Stability analysis for 2D systems with interval timevarying delays and saturation nonlinearities,, Signal Process, 90 (2010), 2265. Google Scholar 
[2] 
S. F. Chen and I. K. Fong, Delaydependent robust stability and stabilization of twodimensional with statedelayed systems,, Dynamics of Continuous, 16 (2009), 1. Google Scholar 
[3] 
S. F. Chen, Delaydependent stability for 2D systems with timevarying delay subject to state saturation in the Roesser model,, Applied Mathematics and Computation, 216 (2010), 2613. doi: 10.1016/j.amc.2010.03.104. Google Scholar 
[4] 
A. Dhawan and H. Kar, Optimal guaranteed cost control of 2D discrete uncertain systems: An LMI approach,, Signal Processing, 87 (2007), 3075. Google Scholar 
[5] 
A. Dhawan and H. Kar, An LMI approach to robust optimal guaranteed cost control of 2D discrete systems described by the Roesser model,, Signal Processing, 90 (2010), 2648. Google Scholar 
[6] 
A. Dhawan and H. Kar, An improved LMIbased criterion for the design of optimal guaranteed cost controller for 2D discrete uncertain systems,, Signal Processing, 91 (2011), 1032. Google Scholar 
[7] 
A. Dhawa and H. Kar, LMIbased criterion for the robust guaranteed cost control of 2D systems described by the FornasiniMarchesini second model,, Signal Process, 87 (2007), 479. Google Scholar 
[8] 
C. Du, L. Xie and C. Zhang, H_{∞} control and robust stabilization of twodimensional system in Roesser models,, Automatica, 37 (2001), 205. doi: 10.1016/S00051098(00)001552. Google Scholar 
[9] 
C. Du and L. Xie, Stability analysis and stabilization of uncertain twodimensional discrete systems: an LMI approach,, IEEE Trans. Circuits Syst. I Fundam. Theory Appl., 46 (1999), 1371. Google Scholar 
[10] 
Z. X. Duan, Z. R Xiang and H. R Karimi, Delaydependent exponential stabilization of positive 2D switched statedelayed systems in the Roesser model,, Information Sciences, 272 (2014), 173. doi: 10.1016/j.ins.2014.02.121. Google Scholar 
[11] 
L. El Ghaoui, F. Oustry and M. AitRami, A cone complementarity linearization algorithm for static outputfeedback and related problems,, IEEE Transactions on Automatic Control, 42 (1997), 1171. doi: 10.1109/9.618250. Google Scholar 
[12] 
X. P. Guan, Z. Y. Lin and G. R. Duan, Robust guaranteed cost control for 2D discrete systems,, IEE Proc. Control Theory Appl., 148 (2001), 355. Google Scholar 
[13] 
T. Hinamoto, Stability of 2D discrete systems described by the FornasiniMarchesini second model,, IEEE Trans. Circuits Syst. I Fundam. Theory Appl., 44 (1997), 254. doi: 10.1109/81.557373. Google Scholar 
[14] 
T. Kaczorek, TwoDimensional Linear System,, Berlin, (1985). Google Scholar 
[15] 
Y. S. Moon, P. Park, W. H. Kwon and Y. S. Lee, Delaydependent robust stabilization of uncertain statedelayed systems,, International Journal of control, 74 (2001), 1447. doi: 10.1080/00207170110067116. Google Scholar 
[16] 
W. Paszke, K. Galkowski, E. Rogers and D. H. Owens, Hinfinity and guaranteed cost control of discrete linear repetitive processes,, Linear Algebra Appl., 412 (2006), 93. doi: 10.1016/j.laa.2005.01.037. Google Scholar 
[17] 
W. Paszke, J. Lam, K. Galkowski, S. Xu and Z. Lin, Robust stability and stabilisation of 2D discrete statedelayed systems,, Syst. Control Lett., 51 (2004), 278. doi: 10.1016/j.sysconle.2003.09.003. Google Scholar 
[18] 
W. Paszke, J. Lam, K. Galkowski, S. Xu and E. Rogers, H_{∞} control of 2D linear statedelayed systems,, in The 4th IFAC Workshop on TimeDelay Systems (France), (2003), 8. Google Scholar 
[19] 
D. Peng, X. Guan and C. Long, Robust output feedback guaranteed cost control for 2D uncertain state delayed systems,, Asian J. Control, 9 (2004), 470. doi: 10.1111/j.19346093.2007.tb00436.x. Google Scholar 
[20] 
D. Peng and X. Guan, Output feedback H_{∞} control for 2D statedelayed systems,, Circuits Syst. Signal Process, 28 (2009), 147. doi: 10.1007/s0003400890743. Google Scholar 
[21] 
L. M. Wang, S. Y. Mo, D. H. Zhou and F. R. Gao, Robust design of feedback integrated with iterative learning control for batch processes with uncertainties and interval timevarying delays,, J. Process Control, 21 (2011), 987. Google Scholar 
[22] 
L. M. Wang, S. Y. Mo, D. H. Zhou, F. R. Gao and X. Chen, Robust delay dependent iterative learning faulttolerant control for batch processes with state delay and actuator failures,, J. Process Control, 22 (2012), 1273. Google Scholar 
[23] 
L. M. Wang, S. Y. Mo, D. H. Zhou, F. R. Gao and X. Chen, Delayrangedependent robust 2D iterative learning control for batch processes with state delay and uncertainties,, J. Process Control, 23 (2013), 715. Google Scholar 
[24] 
L. M. Wang, X. Chen and F. R. Gao, Delayrangedependent robust BIBO stabilization of 2D discrete delayed systems via LMI approach,, In Proceedings of 19th IFAC World Congress, (2014), 10994. Google Scholar 
[25] 
L. Wu, P. Shi, H. Gao and C. Wang, H_{∞} mode reduction for twodimensional discrete statedelayed systems,, IEE Proc. Vis. Image Signal Process, 156 (2006), 769. Google Scholar 
[26] 
J. M. Xu and L. Yu, Delaydependent guaranteed cost control for uncertain 2D discrete systems with state delay in the FM second model,, Journal of the Franklin Institute, 346 (2009), 159. doi: 10.1016/j.jfranklin.2008.08.003. Google Scholar 
[27] 
J. M. Xu and L. Yu, Delaydependent robust H_{∞} control for uncertain 2D discrete statedelay systems in the second FM model,, Multidimensional Syst. Signal Process, 20 (2009), 333. Google Scholar 
[28] 
S. Ye, W. Wang and Y. Zou, Robust guaranteed cost control for class of twodimensional discrete systems with shiftdelays,, Multidimensional Syst. Signal Process, 20 (2009), 297. doi: 10.1007/s1104500800632. Google Scholar 
[29] 
S. X. Ye, J. Z. Li and J. Yao, Robust H_{∞} control for a class of 2D discrete delayed systems,, ISA Transactions, 53 (2015), 1456. Google Scholar 
[30] 
K. W. Yu and C. H. Lien, Stability criteria for uncertain neutral systems with interval timevarying delays,, Chaos, 38 (2008), 650. doi: 10.1016/j.chaos.2007.01.002. Google Scholar 
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