Uniform asymptotic stability of nonlinear switched systems with an application to mobile robots

IEEE Transactions on Automatic Control

Volumn 53, Issue 5, 2008, Pages 1235-1252

  Lee, T C ^a   Jiang, Z P ^b  

^a MINGHSIN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Taiwan)

^b POLYTECHNIC UNIVERSITY   (United States)

Author keywords

Lyapunov functions; Mobile robots; Nonlinear time varying systems; Persistent excitation; Robust regulation; Switched systems; Uniform asymptotic stability; Zero state observability

Indexed keywords

ASYMPTOTIC ANALYSIS; ASYMPTOTIC STABILITY; CONTROL SYSTEM SYNTHESIS; CONTROL THEORY; DIFFERENTIAL EQUATIONS; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; MOBILE ROBOTS; OBSERVABILITY; ROBOTICS; ROBOTS; SWITCHING SYSTEMS; TELECOMMUNICATION NETWORKS; TIME VARYING CONTROL SYSTEMS; TIME VARYING SYSTEMS;

NONLINEAR TIME-VARYING SYSTEMS; PERSISTENT EXCITATION; ROBUST REGULATION; SWITCHED SYSTEMS; UNIFORM ASYMPTOTIC STABILITY; ZERO-STATE OBSERVABILITY;

SYSTEM STABILITY;

EID: 51749083744     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2008.923688     Document Type: Article

References (40)

1. Z. Artstein, "Uniform asymptotic stability via the limiting equations," J. Diff. Eq., vol. 27, pp. 172-189, 1978.
2. A. Bacciotti and L. Mazzi, "An invariance principle for nonlinear switched systems," Syst. Contr. Lett., vol. 54, pp. 1109-1119, 2005.
3. A. Bloch, P. Crouch, J. Baillieul, and J. Marsden, Nonholonomic Mechanics and Control.. New York: Springer-Verlag, 2003.
4. M. S. Branicky, "Multiple lyapunov functions and other analysis tools for switched and hybrid systems," IEEE Trans. Autom. Control, vol. 43, pp. 475-482, 1998.
5. R. A. DeCarlo, M. S. Branicky, S. Pettersson, and B. Lennartson, "Perspectives and results on the stability and stabilizability of hybrid systems," Proc. IEEE, vol. 88, pp. 1069-1082, Jul. 2000.
6. A. Filippov, Differential Equations with Discontinuous Righthand Sides. Dordrecht, Germany: Kluwer, 1988.
7. R. Goebel and A. R. Teel, "Solutions to hybrid inclusions via set and graphical convergence with stability theory applications," Automatica, vol. 42, pp. 573-587, 2006.
8. J. K. Hale, Ordinary Differential Equations. New York: Krieger, 1980.
9. J. P. Hespanha, "Uniform stability of switched linear systems: Extensions of lasalle's invariance principle," IEEE Trans. Autom. Control, vol. 49, no. 3, pp. 470-482, 2004.
10. J. P. Hespanha, D. Liberzon, and A. S. Morse, "Logic-based switching control of a nonholonomic system with parametric modeling uncertainty," Syst. Contr. Lett., vol. 38, pp. 167-177, 1999.
11. J. P. Hespanha, D. Liberzon, and A. S. Morse, "Hysteresis-based switching algorithms for supervisory control of uncertain systems," Automatica, vol. 39, no. 2, pp. 263-272, 2003.
12. J. P. Hespanha, D. Liberzon, and E. D. Sontag, "Nonlinear norm-observability notions and stability of switched systems," IEEE Trans. Autom. Control, vol. 50, no. 2, pp. 154-168, 2005.
13. Z. P. Jiang, "Robust exponential regulation of nonholonomic systems with uncertainties," Automatica, vol. 36, pp. 189-209, 2000.
14. M. Johansson and A. Rantzer, "Computation of piecewise quadratic Lyapunov functions for hybrid systems," IEEE Trans. Autom. Contr. vol. 43, pp. 555-559, Apr. 1998.
15. H. K. Khalil, Nonlinear Systems, 3rd ed. Upper Saddle River, NJ: Prentice-Hall, 2002.
16. I. Kolmanovsky and N. H. McClamroch, "Developments in nonholonomic control problems," IEEE Control Syst. Mag., vol. 15, pp. 20-36, 1995.
17. S. Lang, Real Analysis. Boston, MA: Addison-Wesley, 1983.
18. J. P. LaSalle, "Some extensions of Liapunov's second method," IRE Trans. Circuits Theory, pp. 520-527, 1960, CT-7.
19. T. C. Lee, "Practical stabilization for nonholonomic chained systems with fast convergence, pole-placement and robustness," in Proc. IEEE Int. Conf. Robot. Automat., Washington, DC, 2002, pp. 3534-3539.
20. T. C. Lee, "On the equivalence relations of detectability and PE conditions with applications to stability analysis of time-varying systems," in Proc. Amer. Contr. Conf., Denver, Colorado, 2003, pp. 1873-1878.
21. T. C. Lee and B. S. Chen, "A general stability criterion for time-varying systems using a modified detectability condition," IEEE Trans. Autom. Control, vol. 47, pp. 797-802, 2002.
22. T. C. Lee and Z. P. Jiang, "A generalization of Krasovskii-Lasalle theorem for nonlinear time-varying systems: Converse results and applications," IEEE Trans. Autom. Control, vol. 50, pp. 1147-1163, 2005.
23. D. Liberzon, Switching in Systems and Control. Boston, MA: Birkhäuser, 2003.
24. D. Liberzon, J. P. Hespanha, and A. S. Morse, "Stability of switched systems: A lie-algebraic condition," Syst. Contr. Lett., vol. 37, no. 3, pp. 117-122, Jul. 1999.
25. D. Liberzon and A. S. Morse, "Basic problems in stability and design of switched systems," IEEE Contr. Syst. Mag., vol. 19, no. 10, pp. 59-70, Oct. 1999.
26. D. A. Lizarraga, P. Morin, and C. Samson, "Non-robustness of continuous homogeneous stabilizers for affine control systems," in Proc. IEEE 38th Conf. Dec. Contr., Phoenix, AZ, 1999, pp. 855-860.
27. J. Lygeros, K. H. Johansson, S. M. Simić, J. Zhang, and S. Sastry, "Dynamical properties of hybrid automata," IEEE Trans. Autom. Control, vol. 48, pp. 2-17, 2003.
28. J. L. Mancilla-Aguilar and R. A. García, "A converse Lyapunov theorem for nonlinear switched systems," Syst. Contr. Lett., vol. 41, pp. 67-71, 2000.
29. J. L. Mancilla-Aguilar and R. A. García, "An extension of Lasalle's invariance principle for switched systems," Syst. Contr. Lett., vol. 55, pp. 376-384, 2006.
30. P. Morin and C. Samson, "Robust stabilization of driftless systems with hybrid open-loop/feedback control," in Proc. 2000 Amer. Contr. Conf. Chicago, IL, 2000, pp. 3929-3933.
31. R. Shorten and K. S. Narendra, "On the stability and existence of common Lyapunov functions for linear switching systems," in Proc. 37th IEEE Conf. Dec. Contr., Tampa, FL, Dec. 1998, pp. 3723-3724.
32. J. L. Kelley, General Topology. Berlin, Germany: Springer, 1997.
33. Z. Xi, G. Feng, Z. P. Jiang, and D. Cheng, "A switching algorithm for global exponential stabilization of uncertain chained systems," IEEE Trans. Autom. Control, vol. 48, no. 12, pp. 2212-2217, 2003.
34. E. Panteley, A. Loria, and A. Teel, "Relaxed persistency of excitation for uniform asymptotic stability," IEEE Trans. Autom. Control, vol. 46, pp. 1874-1886, 2001.
35. E. Panteley, R. Ortega, and P. Moya, "Overcoming the detectability obstacle in certainty equivalence adaptive control," Automatica, vol. 38, pp. 1125-1132, 2002.
36. A. Loría, E. Panteley, and K. Melhem, "UGAS of 'skew-symmetric' time-varying systems: Application to stabilization of chained form systems," European J. Contr., vol. 8, pp. 33-43, 2002.
37. A. Teel, E. Panteley, and A. Loria, "Integral characterizations of uniform asymptotic and exponential stability with applications," Math. Contr., Signals Syst., vol. 15, pp. 177-201, 2002.
38. T. C. Lee and Z. P. Jiang, "On uniform global asymptotic stability of nonlinear discrete-time systems with applications," IEEE Trans. Autom. Control, vol. 51, pp. 1644-1660, 2006.
39. 2 - Gain and Passivity Techniques in Nonlinear Control. London, U.K.: Springer, 2000.
40. K. D. Do, Z. P. Jiang, and J. Pan, "A global output-feedback controller for simultaneous tracking and stabilization of unicycle-type mobile robots,," IEEE Trans. Robot. Automat., vol. 20, no. 3, pp. 589-594, 2004.