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Original Articles

Stability of multidimensional systems using bio-inspired meta-heuristics

ORCID Icon, ORCID Icon & ORCID Icon
Pages 2646-2656 | Received 28 Sep 2016, Accepted 11 May 2018, Published online: 29 Jun 2018

References

  • Agathoklis, P., & Mansour, M. (1982, July). Sufficient conditions for instability of two-and higher dimensional discrete systems. IEEE Transactions on Circuits and Systems, 29(7), 486–488. doi: 10.1109/TCS.1982.1085172
  • Anderson, B., & Jury, E. (1974, March). Stability of multidimensional digital filters. IEEE Transactions on Circuits and Systems, 21(2), 300–304. doi: 10.1109/TCS.1974.1083834
  • Bauer, P., & Jury, E. I. (1991, September). BIBO stability of multidimensional (mD) shift-invariant discrete systems. IEEE Transactions on Automatic Control, 36(9), 1057–1061. doi: 10.1109/9.83537
  • Bouzidi, Y., Quadrat, A., & Rouillier, F. (2015). Computer algebra methods for testing the structural stability of multidimensional systems. 2015 IEEE 9th International Workshop on Multidimensional (nd) Systems (nds), Vila Real, Portugal (pp. 11–16). IEEE.
  • Clerc, M., & Kennedy, J. (2002). The particle swarm – explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation, 6(1), 58–73. doi: 10.1109/4235.985692
  • Dabkowski, P., Galkowski, K., Bachelier, O., & Rogers, E. (2012). Control of discrete linear repetitive processes using strong practical stability and disturbance attenuation. Systems & Control Letters, 61(12), 1138–1144. doi: 10.1016/j.sysconle.2012.10.002
  • Dabkowski, P., Galkowski, K., Rogers, E., & Kummert, A. (2007). June. Strong practical stability and control of discrete linear repetitive processes. 2007 International Workshop on Multidimensional (nD) Systems, Aveiro, Portugal (pp. 149–154). IEEE.
  • Eberhart, R., Simpson, P., & Dobbins, R. (1996). Computational intelligence pc tools. San Diego, CA: Academic Press Professional, Inc.
  • Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning (1st ed.). Boston, MA: Addison-Wesley Longman Publishing Co., Inc.
  • Hu, X. (1995, April). Stability tests of N-dimensional discrete time systems using polynomial arrays. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 42(4), 261–268. doi: 10.1109/82.378039
  • Jury, E. I. (1978, September). Stability of multidimensional scalar and matrix polynomials. Proceedings of the IEEE, 66(9), 1018–1047. doi: 10.1109/PROC.1978.11079
  • Jury, E. I. (1985). Stability of multidimensional systems and related problems. In S. Tzafestas (Ed.), Multidimensional systems: Techniques and applications. New York, NY: Marcel-Dekker.
  • Kanellakis, A., Tzafestas, S., & Theodorou, N. (1991, September). Stability tests for 2-D systems using the schwarz form and the inners determinants. IEEE Transactions on Circuits and Systems, 38(9), 1071–1077. doi: 10.1109/31.83877
  • Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. IEEE International Conference on Neural Networks, 1995. Proceedings (Vol. 4, pp. 1942–1948). IEEE.
  • Mann, H. B., & Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. The Annals of Mathematical Statistics, 18(1), 50–60. doi: 10.1214/aoms/1177730491
  • Mastorakis, N. E. (1998, March). A method for computing the 2-D stability margin. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 45(3), 376–379. doi: 10.1109/82.664243
  • Mastorakis, N. E. (2001, November). A new method for computing the stability margin of 2-D discrete systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 48(11), 1363–1365. doi: 10.1109/81.964430
  • Mastorakis, N. E., Gonos, I. F., & Swamy, M. N. S. (2003, July). Stability of multidimensional systems using genetic algorithms. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 50(7), 962–965. doi: 10.1109/TCSI.2003.813968
  • Mastorakis, N. E., Gonos, I. F., & Swamy, M. N. S. (2005, September). Corrections to “stability of multidimensional systems using genetic algorithms”. IEEE Transactions on Circuits and Systems I: Regular Papers, 52(9), 1982–1982. doi: 10.1109/TCSI.2005.852017
  • Matsumoto, N. (1995, April). On some properties of N-D discrete-time BR systems and time-delay br systems. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 42(4), 291–295. doi: 10.1109/82.378045
  • Mezura-Montes, E., Velázquez-Reyes, J., & Coello Coello, C. A. (2006). A comparative study of differential evolution variants for global optimization. Proceedings of the 8th annual conference on genetic and evolutionary computation (pp. 485–492). New York, NY: ACM.
  • Pan, S.-T., & Chen, C.-F. (2008). The robust D-stability analysis of uncertain discrete-delay descriptor systems via genetic algorithms. International Journal of General Systems, 37(3), 305–317. doi: 10.1080/03081070601058737
  • Rogers, E., Galkowski, K., & Owens, D. H. (2007). Control systems theory and applications for linear repetitive processes. Southampton: Springer-Verlag.
  • Roytman, L., Swamy, M., & Eichmann, G. (1987, March). An efficient numerical scheme to compute 2-D stability thresholds. IEEE Transactions on Circuits and Systems, 34(3), 322–324. doi: 10.1109/TCS.1987.1086119
  • Serban, I., & Najim, M. (2007). Multidimensional systems: Bibo stability test based on functional schur coefficients. IEEE Transactions on Signal Processing, 55(11), 5277–5285. doi: 10.1109/TSP.2007.896070
  • Shi, Y., & Eberhart, R. (1998). A modified particle swarm optimizer. IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (cat. no.98th8360), Anchorage, Alaska (pp. 69–73). IEEE.
  • Solteiro Pires, E., de Moura Oliveira, P., & Tenreiro Machado, J. (2015). Meta-heuristics in multidimensional systems stability study. 2015 IEEE 9th International Workshop on Multidimensional (nD) Systems (nDS), Vila Real, Portugal (pp. 1–6). IEEE.
  • Storn, R., & Price, K. (1997). Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces. Journal of Global Optimization, 11(4), 341–359. doi: 10.1023/A:1008202821328
  • Swamy, M., Roytman, L. M., & Plotkin, E. (1985, September). On stability properties of three- and higher dimensional linear shift-invariant digital filters. IEEE Transactions on Circuits and Systems, 32(9), 888–892. doi: 10.1109/TCS.1985.1085812
  • van den Bergh, F., & Engelbrecht, A. P. (2006). A study of particle swarm optimization particle trajectories. Information Sciences, 176(8), 937–971. doi: 10.1016/j.ins.2005.02.003
  • Yang, X. S., & Deb, S. (2009). Cuckoo search via lévy flights. 2009 World Congress on Nature Biologically Inspired Computing (nabic), Coimbatore, India (pp. 210–214).
  • Yost, S. A., & Bauer, P. H. (1995, August). Shift-variant m-D systems and singularities on Tm: implications for robust stability. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 42(8), 477–479. doi: 10.1109/81.404060
  • Zeheb, E. (1984, April). Another simplification in multidimensional stability tests. IEEE Transactions on Acoustics, Speech, and Signal Processing, 32(2), 453–455. doi: 10.1109/TASSP.1984.1164303
  • Zeheb, E., & Hertz, D. (1984, June). Another proof and a generalization of a theorem on N-dimensional stability. Proceedings of the IEEE, 72(6), 745–746. doi: 10.1109/PROC.1984.12927

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