Free Access
Issue
ESAIM: COCV
Volume 26, 2020
Article Number 24
Number of page(s) 16
DOI https://doi.org/10.1051/cocv/2019074
Published online 03 March 2020
  1. J.P. Aubin and A. Cellina, Differential inclusions. Springer (1984). [CrossRef] [Google Scholar]
  2. A. Bacciotti and F. Ceragioli, Stability and stabilization of discontinuous systems and nonsmooth Lyapunov functions. ESAIM: COCV 4 (1999) 361–376. [CrossRef] [EDP Sciences] [Google Scholar]
  3. A. Bacciotti and L. Mazzi, An invariance principle for nonlinear switched systems. Syst. Control Lett. 54 (2005) 1109–1119. [Google Scholar]
  4. F.M. Ceragioli, Discontinuous ordinary differential equations and stabilization. Ph.D. thesis, Universita di Firenze, Italy (1999). [Google Scholar]
  5. F.H. Clarke, Optimization and nonsmooth analysis. SIAM (1990). [CrossRef] [Google Scholar]
  6. A.F. Filippov, Differential equations with discontinuous right-hand sides. Kluwer Academic Publishers (1988). [CrossRef] [Google Scholar]
  7. N. Fischer, R. Kamalapurkar and W.E. Dixon, LaSalle-Yoshizawa corollaries for nonsmooth systems. IEEE Trans. Autom. Control 58 (2013) 2333–2338. [CrossRef] [Google Scholar]
  8. W.M. Haddad, V. Chellaboina and S.G. Nersesov, Impulsive and hybrid dynamical systems, Princeton Series in Applied Mathematics (2006). [Google Scholar]
  9. Q. Hui, W.M. Haddad and S.P. Bhat, Semistability, finite-time stability, differential inclusions, and discontinuous dynamical systems having a continuum of equilibria. IEEE Trans. Autom. Control 54 (2009) 2465–2470. [CrossRef] [Google Scholar]
  10. R. Kamalapurkar, W.E. Dixon and A.R. Teel, On reduction of differential inclusions and Lyapunov stability, in Proc. IEEE Conf. Decis. Control, Melbourne, VIC, Australia (2017) 5499–5504. [Google Scholar]
  11. R. Kamalapurkar, W.E. Dixon and A.R. Teel, On reduction of differential inclusions and Lyapunov stability. Preprint arXiv:1703.07071 (2018). [Google Scholar]
  12. H.K. Khalil, Nonlinear systems, 3rd edition. Prentice Hall, Upper Saddle River, NJ (2002). [Google Scholar]
  13. N.N. Krasovskii and A.I. Subbotin, Game-theoretical control problems. Springer-Verlag, New York (1988). [Google Scholar]
  14. H. Logemann and E. Ryan, Asymptotic behaviour of nonlinear systems. Am. Math. Mon. 111 (2004) 864–889. [Google Scholar]
  15. A. Loría, E. Panteley, D. Popovic and A.R. Teel, A nested Matrosov theorem and persistency of excitation for uniform convergence in stable nonautonomous systems. IEEE Trans. Autom. Control 50 (2005) 183–198. [CrossRef] [Google Scholar]
  16. V.M. Matrosov, On the stability of motion. J. Appl. Math. Mech. 26 (1962) 1337–1353. [CrossRef] [Google Scholar]
  17. A.N. Michel and K. Wang, Qualitative theory of dynamical systems, the role of stability preserving mappings. Marcel Dekker, New York (1995). [Google Scholar]
  18. J.J. Moreau and M. Valadier, A chain rule involving vector functions of bounded variation. J. Funct. Anal. 74 (1987) 333–345. [Google Scholar]
  19. E. Moulay and W. Perruquetti, Finite time stability of differential inclusions. IMA J. Math. Control Inf . 22 (2005) 465–275. [CrossRef] [Google Scholar]
  20. B.E. Paden and S.S. Sastry, A calculus for computing Filippov’s differential inclusion with application to the variable structure control of robot manipulators. IEEE Trans. Circuits Syst. 34 (1987) 73–82. [CrossRef] [Google Scholar]
  21. B. Paden and R. Panja, Globally asymptotically stable ‘PD+’ controller for robot manipulators. Int. J. Control 47 (1988) 1697–1712. [Google Scholar]
  22. R.T. Rockafellar and R.J.-B. Wets, Vol. 317 of Variational analysis. Springer Science & Business Media (2009). [Google Scholar]
  23. E. Roxin, Stability in general control systems. J. Differ. Equ. 1 (1965) 115–150. [Google Scholar]
  24. W. Rudin, Principles of mathematical analysis. McGraw-Hill (1976). [Google Scholar]
  25. E.P. Ryan, Discontinuous feedback and universal adaptive stabilization, in Control of Uncertain systems. Springer (1990) 245–258. [CrossRef] [Google Scholar]
  26. E. Ryan, An integral invariance principle for differential inclusions with applications in adaptive control. SIAM J. Control Optim. 36 (1998) 960–980. [Google Scholar]
  27. R. Sanfelice and A.R. Teel, Asymptotic stability in hybrid systems via nested Matrosov functions. IEEE Trans. Autom. Control 54 (2009) 1569–1574. [CrossRef] [Google Scholar]
  28. D. Shevitz and B. Paden, Lyapunov stability theory of nonsmooth systems. IEEE Trans. Autom. Control 39 (1994) 1910–1914. [CrossRef] [MathSciNet] [Google Scholar]
  29. A.R. Teel, D. Nešić, T.-C. Lee and Y. Tan, A refinement of Matrosov’s theorem for differential inclusions. Automatica 68 (2016) 378–383. [CrossRef] [Google Scholar]
  30. M. Vidyasagar, Nonlinear systems analysis, 2nd edition. SIAM (2002). [CrossRef] [Google Scholar]

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