Free Access
Volume 5, 2000
Page(s) 313 - 367
Published online 15 August 2002
  1. A.N. Atassi and H.K. Khalil, A separation principle for the control of a class of nonlinear systems, in Proc. of the 37th IEEE Conference on Decision and Control. Tampa, FL (1998) 855-860. [Google Scholar]
  2. J.-P. Aubin and A. Cellina, Differential Inclusions: Set-valued Maps and Viability Theory. Springer-Verlag, New York (1984). [Google Scholar]
  3. J.-P. Aubin and H. Frankowska, Set-valued Analysis. Birkhauser, Boston (1990). [Google Scholar]
  4. A. Bacciotti and L. Rosier, Lyapunov and Lagrange stability: Inverse theorems for discontinuous systems. Math. Control Signals Systems 11 (1998) 101-128. [CrossRef] [MathSciNet] [Google Scholar]
  5. E.A. Barbashin and N.N. Krasovskii, On the existence of a function of Lyapunov in the case of asymptotic stability in the large. Prikl. Mat. Mekh. 18 (1954) 345-350. [Google Scholar]
  6. F.H. Clarke, Y.S. Ledyaev and R.J. Stern, Asymptotic stability and smooth Lyapunov functions. J. Differential Equations 149 (1998) 69-114. [CrossRef] [MathSciNet] [Google Scholar]
  7. F.H. Clarke, Y.S. Ledyaev, R.J. Stern and P.R. Wolenski, Nonsmooth Analysis and Control Theory. Springer (1998). [Google Scholar]
  8. F.H. Clarke, R.J. Stern and P.R. Wolenski, Subgradient criteria for monotonicity, the Lipschitz condition, and convexity. Canad. J. Math. 45 (1993) 1167-1183. [CrossRef] [MathSciNet] [Google Scholar]
  9. W.P. Dayanwansa and C.F. Martin, A converse Lyapunov theorem for a class of dynamical systems which undergo switching. IEEE Trans. Automat. Control 44 (1999) 751-764. [CrossRef] [MathSciNet] [Google Scholar]
  10. K. Deimling, Multivalued Differential Equations. Walter de Gruyter, Berlin (1992). [Google Scholar]
  11. A.F. Filippov, On certain questions in the theory of optimal control. SIAM J. Control 1 (1962) 76-84. [Google Scholar]
  12. A.F. Filippov, Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publishers (1988). [Google Scholar]
  13. W. Hahn, Stability of Motion. Springer-Verlag (1967). [Google Scholar]
  14. F.C. Hoppensteadt, Singular perturbations on the infinite interval. Trans. Amer. Math. Soc. 123 (1966) 521-535. [CrossRef] [MathSciNet] [Google Scholar]
  15. J. Kurzweil, On the inversion of Ljapunov's second theorem on stability of motion. Amer. Math. Soc. Trans. Ser. 2 24 (1956) 19-77. [Google Scholar]
  16. V. Lakshmikantham, S. Leela and A.A. Martynyuk, Stability Analysis of Nonlinear Systems. Marcel Dekker, Inc. (1989). [Google Scholar]
  17. V. Lakshmikantham and L. Salvadori, On Massera type converse theorem in terms of two different measures. Bull. U.M.I. 13 (1976) 293-301. [Google Scholar]
  18. Y. Lin, E.D. Sontag and Y. Wang, A smooth converse Lyapunov theorem for robust stability. SIAM J. Control Optim. 34 (1996) 124-160. [CrossRef] [MathSciNet] [Google Scholar]
  19. A.M. Lyapunov, The general problem of the stability of motion. Math. Soc. of Kharkov, 1892 (Russian). [English Translation: Internat. J. Control 55 (1992) 531-773]. [Google Scholar]
  20. I.G. Malkin, On the question of the reciprocal of Lyapunov's theorem on asymptotic stability. Prikl. Mat. Mekh. 18 (1954) 129-138. [Google Scholar]
  21. J.L. Massera, On Liapounoff's conditions of stability. Ann. of Math. 50 (1949) 705-721. [CrossRef] [MathSciNet] [Google Scholar]
  22. J.L. Massera, Contributions to stability theory. Ann. of Math. 64 (1956) 182-206. (Erratum: Ann. of Math. 68 (1958) 202.) [CrossRef] [MathSciNet] [Google Scholar]
  23. A.M. Meilakhs, Design of stable control systems subject to parametric perturbations. Avtomat. i Telemekh. 10 (1978) 5-16. [Google Scholar]
  24. A.P. Molchanov and E.S. Pyatnitskii, Lyapunov functions that specify necessary and sufficient conditions of absolute stability of nonlinear nonstationary control systems I. Avtomat. i Telemekh. (1986) 63-73. [Google Scholar]
  25. A.P. Molchanov and E.S. Pyatnitskiin, Lyapunov functions that specify necessary and sufficient conditions of absolute stability of nonlinear nonstationary control systems II. Avtomat. i Telemekh. (1986) 5-14. [Google Scholar]
  26. A.P. Molchanov and E.S. Pyatnitskii, Criteria of asymptotic stability of differential and difference inclusions encountered in control theory. Systems Control Lett. 13 (1989) 59-64. [CrossRef] [MathSciNet] [Google Scholar]
  27. A.A. Movchan, Stability of processes with respect to two measures. Prikl. Mat. Mekh. (1960) 988-1001. [Google Scholar]
  28. I.P. Natanson, Theory of Functions of a Real Variable. Vol. 1. Frederick Ungar Publishing Co. (1974). [Google Scholar]
  29. E.P. Ryan, Discontinuous feedback and universal adaptive stabilization, in Control of Uncertain Systems, edited by D. Hinrichsen and B. Martensson. Birkhauser, Boston (1990) 245-258. [Google Scholar]
  30. E.D. Sontag, Comments on integral variants of ISS. Systems Control Lett. 34 (1998) 93-100. [CrossRef] [MathSciNet] [Google Scholar]
  31. E.D. Sontag and Y. Wang, A notion of input to output stability, in Proc. European Control Conf. Brussels (1997), Paper WE-E A2, CD-ROM file ECC958.pdf. [Google Scholar]
  32. E.D. Sontag and Y. Wang, Notions of input to output stability. Systems Control Lett. 38 (1999) 235-248. [CrossRef] [MathSciNet] [Google Scholar]
  33. E.D. Sontag and Y. Wang, Lyapunov characterizations of input to output stability. SIAM J. Control Optim. (to appear). [Google Scholar]
  34. A.M. Stuart and A.R. Humphries, Dynamical Systems and Numerical Analysis. Cambridge University Press, New York (1996). [Google Scholar]
  35. A.R. Teel and L. Praly, Tools for semiglobal stabilization by partial state and output feedback. SIAM J. Control Optim. 33 (1995) 1443-1488. [CrossRef] [MathSciNet] [Google Scholar]
  36. J. Tsinias, A Lyapunov description of stability in control systems. Nonlinear Anal. 13 (1989) 63-74. [CrossRef] [MathSciNet] [Google Scholar]
  37. J. Tsinias and N. Kalouptsidis, Prolongations and stability analysis via Lyapunov functions of dynamical polysystems. Math. Systems Theory 20 (1987) 215-233. [CrossRef] [MathSciNet] [Google Scholar]
  38. J. Tsinias, N. Kalouptsidis and A. Bacciotti, Lyapunov functions and stability of dynamical polysystems. Math. Systems Theory 19 (1987) 333-354. [CrossRef] [MathSciNet] [Google Scholar]
  39. V.I. Vorotnikov, Stability and stabilization of motion: Research approaches, results, distinctive characteristics. Avtomat. i Telemekh. (1993) 3-62. [Google Scholar]
  40. F.W. Wilson, Smoothing derivatives of functions and applications. Trans. Amer. Math. Soc. 139 (1969) 413-428. [CrossRef] [MathSciNet] [Google Scholar]
  41. T. Yoshizawa, Stability Theory by Lyapunov's Second Method. The Mathematical Society of Japan (1966). [Google Scholar]
  42. K. Yosida, Functional Analysis, 2nd Edition. Springer Verlag, New York (1968). [Google Scholar]

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