OBSERVER FOR A CLASS OF STOCHASTICALLY PERTURBED LIPSCHITZ NONLINEAR SYSTEMS

Tua A. Tamba and Yul Y. Nazaruddin

References

  1. [1] P.V. Kokotovi´c and M. Arcak, Constructive nonlinear control: a historical perspective, Automatica, 37(5), 2001, 637–662.
  2. [2] A.P. Dani, S.-J. Chung, and S. Hutchinson, Observer design for stochastic nonlinear systems via contraction-based incremental stability, IEEE Transactions on Automatic Control, 60(3), 2015, 700–714.
  3. [3] F.E. Thau, Observing the state of nonlinear dynamic systems, International Journal of Control, 17(3), 1973, 471–479.
  4. [4] S. Raghavan and J.K. Hedrick, Observer design for a class of nonlinear systems, International Journal of Control, 59(2), 1994, 515–528.
  5. [5] R. Rajamani, Observers for Lipschitz nonlinear systems, IEEE Transactions on Automatic Control, 43(3), 1998, 397–401.
  6. [6] C. Aboky, G. Sallet, and J.-C. Vivalda, Observers for Lipschitz nonlinear systems, International Journal of Control, 75(3), 2002, 204–212.
  7. [7] K. Ma, F. He, and Y. Yao, Observer design for Lipschitznonlinear systems, Control & Intelligent Systems, 37(2), 2009, 97–102.
  8. [8] A. Zemouche and M. Boutayeb, On LMI conditions to design observers for Lipschitz nonlinear systems, Automatica, 49(2), 2013, 585–591.
  9. [9] M. Abbaszadeh and H.J. Marquez, Robust H∞ observer design for sampled-data Lipschitz nonlinear systems with exact and Euler approximate models, Automatica, 44(3), 2008, 799–806.
  10. [10] A.M. Pertew, H.J. Marquez, and Q. Zhao, H∞ observerdesign for Lipschitz nonlinear systems, IEEE Transactions on Automatic Control, 51(7), 2006, 1211–1216.
  11. [11] S.P. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory (Philadelphia, USA: SIAM, 1994).
  12. [12] T.J. Tarn and Y. Rasis, Observers for nonlinear stochastic systems, IEEE Transactions on Automactic Control, 21(4), 1976, 441–448.
  13. [13] E. Yaz and A. Azemi, Observer design for discrete and continuous nonlinear stochastic systems, International Journal of Systems Science, 24(12), 1993, 2289–2302.
  14. [14] A.S. Poznyak, R. Martinez-Guerra, and A. Osorio-Cordero, Robust high-gain observer for nonlinear closed-loop stochastic systems, Mathematical Problems in Engineering, 6(1), 2000, 31-60.
  15. [15] A.S. Poznyak, A. Nazin, and D. Murano, Observer matrix gain optimization for stochastic continuous time nonlinear systems, Systems and Control Letters, 52(5), 2004, 377–385.
  16. [16] A. Barbata, M. Zasadzinski, H. Souley Ali, and H. Mes-saoud, Exponential observer for a class of one-sided Lipschitz stochastic nonlinear systems, IEEE Transactions on Automatic Control, 60(1), 2015, 259–264.
  17. [17] X.-F. Miao, L.-S. Li, and X.-M. Yan, Adaptive state estimation for a class of nonlinear stochastic systems under generalized Lipschitz condition, International Journal of Theoretical Physics, 53(11), 2014, 3935–3942.
  18. [18] X. Miao and L. Li, Adaptive observer-based control for a class of nonlinear stochastic systems, International Journal of Computer Mathematics, 92(11), 2014, 1–10.
  19. [19] L. Xie and P. Khargonekar, Lyapunov-based adaptive state estimation for a class of nonlinear stochastic systems, Automatica, 48(7), 2012, 1423–1431.
  20. [20] M. Zakai, On the ultimate boundedness of moments associated with solutions of stochastic differential equations, SIAM Journal of Control, 5(4), 1967, 588–593.
  21. [21] Y. Miyahara, Ultimate boundedness of the systems governed by stochastic differential equations, Nagoya Mathematical Journal, 48, 1972, 111–144.
  22. [22] T.A Tamba and A. Turnip, Observer design for a class of nonlinear systems driven by stochastic process with bounded covariance, Proc. 15th International Conf. on Control, Automation and Systems, Busan, South Korea, 2015, 1128–1132.
  23. [23] R. Khasminskii, Stochastic Stability of Differential Equations (New York, USA: Springer, 2011).
  24. [24] X. Mao, Stochastic Differential Equations and Applications (Amsterdam, Netherlands: Elsevier, 2007).
  25. [25] J. Lofberg, YALMIP: a toolbox for modeling and optimization in MATLAB, Proc. IEEE International Symposium on Computer Aided Control Systems Design, Taipei, Taiwan, 2004, 284–289.
  26. [26] A.J. Koshkouei and A.S.I. Zinober, Sliding mode state observation for nonlinear systems, International Journal of Control, 77(2), 2004, 118–127.
  27. [27] A.P.S. Mosek, The MOSEK optimization software, http://www.mosek.com (2010).
  28. [28] T.A. Tamba and Y.Y. Nazaruddin, Stochastic stability of dynamical systems driven by L´evy processes, Control andIntelligent Systems, 44(2), 2016, 65–75.
  29. [29] T.A. Tamba and M.D. Lemmon, Using first passage times to manage eco-system regime shifts, Proc. 52nd IEEE Conf. on Decision and Control, Trieste, Italy, 2013, 2697–2702.
  30. [30] H. Li, Y. Gao, P. Shi, Peng, and H.-K. Lam, Observerbased fault detection for nonlinear systems with sensor fault and limited communication capacity, IEEE Transactions on Automatic Control, 61(9), 2016, 2745–2751.
  31. [31] A. Hocine, M. Chadli, D. Maquin, and J. Ragot, A discrete-time sliding window observer for Markovian switching system: an LMI approach, Control & Intelligent Systems, 36(2), 2008, 174–181.
  32. [32] H. Li, P. Shi, D. Yao, and L. Wu, Observer-based adaptive sliding mode control for nonlinear Markovian jump systems, Automatica, 64, 2016, 133–142.
  33. [33] Q. Zhou, P. Shi, S. Xu, and H. Li, Observer-based adaptive neural network control for nonlinear stochastic systems with time delay, IEEE Transactions on Neural Networks and Learning Systems, 24(1), 2013, 71-80.
  34. [34] A. Ismail, M. S. Mahmoud, and P. Shi, Output feedbackstabilization and disturbance attenuation of time-delay systems with Markovian jump parameters, Control and Intelligent Systems, 32(3), 2004, 193–206.

Important Links:

Go Back