Semi-Global Practical Stability of Random Systems and Its Application

1. Liu X Z, Practical stabilization of control systems with impulse effects, Journal of Mathematical Analysis and Applications, 1992, 166(2): 563–576.

   Article  MathSciNet  MATH  Google Scholar 

2. Yang X S, Practical stability in dynamical systems, Chaos, Solitons and Fractals, 2000, 11(7): 1087–1092.

   Article  MathSciNet  MATH  Google Scholar 

3. Errebii M, Ellouze I, and Hammami M A, Exponential convergence of nonlinear time-varying differential equations, Journal of Contemporary Mathematical Analysis, 2015, 50(4): 167–175.

   Article  MathSciNet  MATH  Google Scholar 

4. Khalil H K, Nonlinear Control, Pearson Education Inc, New York, 2015.

   Google Scholar 

5. Chen H, Wang C L, Liang Z Y, et al., Robust practical stabilization of nonholonomic mobile robots based on visual servoing feedback with inputs saturation, Asian Journal of Control, 2014, 16(3): 692–702.

   Article  MathSciNet  MATH  Google Scholar 

6. Moreau L and Aeyels D, Practical stability and stabilization, IEEE Transactions on Automatic Control, 2000, 45(8): 1554–1558.

   Article  MathSciNet  MATH  Google Scholar 

7. Sanchez C A, Garcia G, Hadjeras S, et al., Practical stabilization of switched affine systems with dwell-time guarantees, IEEE Transactions on Automatic Control, 2019, 64(11): 4811–4817.

   Article  MathSciNet  MATH  Google Scholar 

8. Jin S L, Liu Y G, and Li F Z, Global practical tracking for nonlinear systems with more unknowns via adaptive output-feedback, Asian Journal of Control, 2017, 20(4): 1–17.

   MathSciNet  Google Scholar 

9. Huang Y X and Liu Y G, Practical tracking via adaptive event-triggered feedback for uncertain nonlinear systems, IEEE Transactions on Automatic Control, 2019, 64(9): 3920–3927.

   Article  MathSciNet  MATH  Google Scholar 

10. Li F Z and Liu Y G, Global practical tracking with prescribed transient performance for inherently nonlinear systems with extremely severe uncertainties, Science in China: Information Science, 2019, 62(2): 1–16.

    MathSciNet  Google Scholar 

11. Khalil H and Esfandiari F, Semiglobal stabilization of a class of nonlinear systems using output feedback, IEEE Transactions on Automatic Control, 1993, 38(9): 1412–1415.

    Article  MathSciNet  MATH  Google Scholar 

12. Pettersen K Y and Nijmeijer H, Semi-global practical stabilization and disturbance adaptation for an underactuated ship, Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, 2000.

13. Soro D and Lozano R, Semi-global practical stabilization of an underactuated surface vessel via nested saturation controller, Proceedings of the American Control Conference, Denver, 2003.

14. Wang C, Semiglobal practical stabilization of nonholonomic wheeled mobile robots with saturated inputs, Automatica, 2008, 44(3): 816–822.

    Article  MathSciNet  MATH  Google Scholar 

15. Chaillet A and Loría A, Necessary and sufficient conditions for uniform semiglobal practical asymptotic stability: Application to cascaded systems, Automatica, 2006, 42(11): 1899–1906.

    Article  MathSciNet  MATH  Google Scholar 

16. Chaillet A and Loría A, Uniform semiglobal practical asymptotic stability for non-autonomous cascaded systems and applications, Automatica, 2008, 44(2): 337–347.

    Article  MathSciNet  MATH  Google Scholar 

17. Ge S S and Wang C, Direct adaptive nn control of a class of nonlinear systems, IEEE Transactions on Neural Networks, 2002, 13(1): 214–221.

    Article  Google Scholar 

18. Ge S S and Wang C, Adaptive neural control of uncertain MIMO nonlinear systems, IEEE Transictionson Neural Networks, 2004, 15(3): 674–692.

    Article  Google Scholar 

19. Liu X P, Wang H Q, Gao C, et al., Adaptive fuzzy funnel control for a class of strict feedback nonlinear systems, Neurocomputing, 2017, 241(7): 71–80.

    Article  Google Scholar 

20. Liu C G, Liu X P, Wang H Q, et al., Observer-based adaptive fuzzy funnel control for strict-feedback nonlinear systems with unknown control coefficients, Neurocomputing, 2019, 358(17): 467–478.

    Article  Google Scholar 

21. Xie X J, Li Z J, and Zhang K M, Semi-global output feedback control for nonlinear systems with uncertain time-delay and output function, International Journal of Robust and Nonlinear Control, 2016, 27(15): 2549–2566.

    Article  MathSciNet  MATH  Google Scholar 

22. Li R R and Hong Y G, Semi-global cooperative output regulation of a class of nonlinear uncertain multi-agent systems under switching networks, International Journal of Robust and Nonlinear Control, 2017, 27(18): 5061–5081.

    Article  MathSciNet  MATH  Google Scholar 

23. Su Y F, Semi-global output feedback cooperative control for nonlinear multi-agent systems via internal model approach, Automatica, 2019, 103: 200–207.

    Article  MathSciNet  MATH  Google Scholar 

24. Liu W and Huang J, Sampled-data semi-global robust output regulation for a class of nonlinear systems, Journal of Systems Science & Complexity, 2021, 34(5): 1743–1765.

    Article  MathSciNet  MATH  Google Scholar 

25. Krstić M, Kokotović P V, and Kanellakopoulos I, Nonlinear and Adaptive Control Design, Wiley, New York, 1995.

    MATH  Google Scholar 

26. Swaroop D, Hedrick J K, Yip P P, et al., Dynamic surface control for a class of nonlinear systems, IEEE Transactions on Automatic Control, 2000, 45(10): 1893–1899.

    Article  MathSciNet  MATH  Google Scholar 

27. Farrell J A, Polycarpou M, Sharma M, et al., Command filtered backstepping, IEEE Transactions on Automatic Control, 2009, 54(6): 1391–1395.

    Article  MathSciNet  MATH  Google Scholar 

28. Khasminskii R, Stochastic Stability of Differential Equations, Springer Science & Business Media, Rockville, 1980.

    Book  MATH  Google Scholar 

29. Wu Z J, Stability criteria of random nonlinear systems and their applications, IEEE Transactions on Automatic Control, 2015, 60(4): 1038–1049.

    Article  MathSciNet  MATH  Google Scholar 

30. Wu Z J, Karimi H R, and Shi P, Practical trajectory tracking of random Lagrange systems, Automatica, 2019, 105: 314–322.

    Article  MathSciNet  MATH  Google Scholar 

31. Yip P P and Hedrick J K, Adaptive dynamic surface control: A simplified algorithm for adaptive backstepping control of nonlinear systems, International Journal of Control, 1998, 71(5): 959–979.

    Article  MathSciNet  MATH  Google Scholar 

32. Khalil H K, Nonlinear Systems, Prentice Hall, Englewood Cliff, 2002.

    MATH  Google Scholar 

33. Pan Z G and Başar T, Backstepping controller design for nonlinear stochastic systems under a risk-sensitive cost criterion, SIAM Journal on Control and Optimization, 1999, 37(3): 957–995.

    Article  MathSciNet  MATH  Google Scholar 

34. Yu X and Wu Z J, Corrections to “stochastic barbalat’s lemma and its applications”, IEEE Transactions on Automatic Control, 2014, 59(5): 1386–1390.

    Article  MathSciNet  MATH  Google Scholar 

35. Cui M Y, Wu Z J, and Xie X J, Stochastic modeling and tracking control for a two-link planar rigid robot manipulator, International Journal of Innovative Computing, Information and Control, 2013, 9(4): 1769–1780.

    Google Scholar 

36. Cui M Y and Wu Z J, Trajectory tracking of flexible joint manipulators actuated by DC-motors under random disturbances, Journal of the Franklin Institute, 2019, 356(16): 9330–9343.

    Article  MathSciNet  MATH  Google Scholar 

37. Spong M W, Seth H, and Vidyasagar M, Robot Modeling and Control, John Wiley & Sons Inc, New York, 2006.

    Google Scholar 

38. Ortega R, Loría A, Nicklasson P J, et al., Passivity-Based Control of Euler-Lagrange Systems: Mechanical, Electrical and Electromechanical Applications, Springer-Verlag, Berlin, 1998.

    Book  Google Scholar 

Download references