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Filtering Homogeneous Observer for MIMO System (2401.03135v1)

Published 6 Jan 2024 in eess.SY and cs.SY

Abstract: Homogeneous observer for linear multi-input multi-output (MIMO) system is designed. A prefilter of the output is utilized in order to improve robustness of the observer with respect to measurement noises. The use of such a prefilter also simplifies tuning, since the observer gains in this case are parameterized by a linear matrix inequality (LMI) being always feasible for observable system. In particular case, the observer is shown to be applicable in the presence of the state and the output bounded perturbations. Theoretical results are supported by numerical simulations.

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References (41)
  1. On inherent limitations in robustness and performance for a class of prescribed-time algorithms. Automatica, 158:111284, 2023.
  2. Homogeneous Approximation, Recursive Observer Design, and Output Feedback. SIAM Journal of Control and Optimization, 47(4):1814–1850, 2008.
  3. Geometric homogeneity with applications to finite-time stability. Mathematics of Control, Signals and Systems, 17:101–127, 2005.
  4. Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM, 1994.
  5. E. Cruz-Zavala and J. A. Moreno. Homogeneous high order sliding mode design: A lyapunov approach. Automatica, 80(6):232–238, 2017.
  6. Uniform robust exact differentiator. IEEE Transactions on Automatic Control, 56(11):2727–2733, 2011.
  7. D. Efimov and A. Polyakov. Finite-time stability tools for control and estimation. Foundations and Trends in Systems and Control. Netherlands: now Publishers Inc, 2021.
  8. A. F. Filippov. Differential Equations with Discontinuous Right-hand Sides. Kluwer Academic Publishers, 1988.
  9. V. Fischer and M. Ruzhansky. Quantization on Nilpotent Lie Groups. Springer, 2016.
  10. H. Hermann and A. Krener. Nonlinear controllability and observability. IEEE Transactions on Automatic Control, 22(728-740), 1977.
  11. J. Holloway and M. Krstic. Prescribed-time observers for linear systems in observer canonical form. IEEE Transactions on Automatic Control, 64(9):3905–3912, 2019.
  12. Y. Hong. H∞{}_{\infty}start_FLOATSUBSCRIPT ∞ end_FLOATSUBSCRIPT control, stabilization, and input-output stability of nonlinear systems with homogeneous properties. Automatica, 37(7):819–829, 2001.
  13. L.S. Husch. Topological Characterization of The Dilation and The Translation in Frechet Spaces. Mathematical Annals, 190:1–5, 1970.
  14. A. Isidori. Nonlinear Control Systems. Springer-Verlag, N. Y. Inc., 1995.
  15. Filtering homogeneous observers in control of integrator chains. International Journal of Robust and Nonlinear Control, 31(9):3658–3685, 2021.
  16. M. Kawski. Families of dilations and asymptotic stability. Analysis of Controlled Dynamical Systems, pages 285–294, 1991.
  17. H. K. Khalil and L. Praly. High-gain observers in nonlinear feedback control. International Journal of Robust and Nonlinear Control, 24(6):993–1015, 2014.
  18. G. Kreisselmeier and R. Engel. Nonlinear observers for autonomous lipschitz continuous systems. IEEE Transactions on Automatic Control, 48(3):451–464, 2003.
  19. A. Levant. Robust exact differentiation via sliding mode technique. Automatica, 34(3):379–384, 1998.
  20. A. Levant. Higher-order sliding modes, differentiation and output-feedback control. International Journal of Control, 76(9-10):924–941, 2003.
  21. Generalized extended state observer based control for systems with mismatched uncertainties. IEEE Transaction on Industrial Electronics, 59(12):4792–4802, 2012.
  22. Finite-time and fixed-time observer design: Implicit Lyapunov function approach. Automatica, 87(1):52–60, 2018.
  23. D. Luenberger. Observing the state of a linear system. IEEE Transactions on Military Electronics, 8(2):74–80, 1964.
  24. J. A. Moreno. Arbitrary-order fixed-time differentiators. IEEE Transaction on Automatic Control, 67(3):1543–1549, 2022.
  25. J. A. Moreno. High-order sliding-mode functional observers for multiple-input multiple-output (mimo) linear time-invariant systems with unknown inputs. International Journal of Robust and Nonlinear Control, 33(15):8844–8869, 2023.
  26. On simple design of a robust finite-time observer. In Conference on Decision and Control, 2022.
  27. A. Pazy. Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer, 1983.
  28. Finite-time observers: application to secure communication. IEEE Transactions on Automatic Control, 53(1):356–360, 2008.
  29. A. Polyakov. Generalized Homogeneity in Systems and Control. Springer, 2020.
  30. Robust stabilization of MIMO systems in finite/fixed time. International Journal of Robust and Nonlinear Control, 26(1):69–90, 2016.
  31. B. Poyak and M.V. Topunov. Suppression of bounded exogenous disturbances: output feedback. Automation and Remote Control, 69(5):801–818, 2008.
  32. L. Rosier. Homogeneous Lyapunov function for homogeneous continuous vector field. Systems & Control Letters, 19:467–473, 1992.
  33. E.P. Ryan. Universal stabilization of a class of nonlinear systems with homogeneous vector fields. Systems & Control Letters, 26:177–184, 1995.
  34. Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time. Automatica, 83:243–251, 2017.
  35. E.D. Sontag. Smooth stabilization implies coprime factorization. IEEE Transactions on Automatic Control, 34:435–443, 1989.
  36. E.D. Sontag and Y. Wang. On characterizations of the input-to-state stability property. Systems & Control Letters, 24(5):351–359, 1996.
  37. W. M. Wonham. Linear Multivariable Control: A Geometric Approach. Springer, 1985.
  38. Fixed-time stabilization of linear delay systems by smooth periodic delayed feedback. IEEE Transactions on Automatic Control, 67(2):557–573, 2022.
  39. Robust feedback stabilization of linear mimo systems using generalized homogenization. IEEE Transactions on Automatic Control, 2020.
  40. V. I. Zubov. Methods of A.M. Lyapunov and Their Applications. Noordhoff, Leiden, 1964.
  41. V. I. Zubov. On systems of ordinary differential equations with generalized homogeneous right-hand sides. Izvestia vuzov. Mathematica (in Russian), 1:80–88, 1958.

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