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.
  2. J.-P. Aubin and A. Cellina, Differential Inclusions: Set-valued Maps and Viability Theory. Springer-Verlag, New York (1984).
  3. J.-P. Aubin and H. Frankowska, Set-valued Analysis. Birkhauser, Boston (1990).
  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]
  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.
  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]
  7. F.H. Clarke, Y.S. Ledyaev, R.J. Stern and P.R. Wolenski, Nonsmooth Analysis and Control Theory. Springer (1998).
  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]
  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]
  10. K. Deimling, Multivalued Differential Equations. Walter de Gruyter, Berlin (1992).
  11. A.F. Filippov, On certain questions in the theory of optimal control. SIAM J. Control 1 (1962) 76-84.
  12. A.F. Filippov, Differential Equations with Discontinuous Righthand Sides. Kluwer Academic Publishers (1988).
  13. W. Hahn, Stability of Motion. Springer-Verlag (1967).
  14. F.C. Hoppensteadt, Singular perturbations on the infinite interval. Trans. Amer. Math. Soc. 123 (1966) 521-535. [CrossRef] [MathSciNet]
  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.
  16. V. Lakshmikantham, S. Leela and A.A. Martynyuk, Stability Analysis of Nonlinear Systems. Marcel Dekker, Inc. (1989).
  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.
  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]
  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].
  20. I.G. Malkin, On the question of the reciprocal of Lyapunov's theorem on asymptotic stability. Prikl. Mat. Mekh. 18 (1954) 129-138.
  21. J.L. Massera, On Liapounoff's conditions of stability. Ann. of Math. 50 (1949) 705-721. [CrossRef] [MathSciNet]
  22. J.L. Massera, Contributions to stability theory. Ann. of Math. 64 (1956) 182-206. (Erratum: Ann. of Math. 68 (1958) 202.) [CrossRef] [MathSciNet]
  23. A.M. Meilakhs, Design of stable control systems subject to parametric perturbations. Avtomat. i Telemekh. 10 (1978) 5-16.
  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.
  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.
  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]
  27. A.A. Movchan, Stability of processes with respect to two measures. Prikl. Mat. Mekh. (1960) 988-1001.
  28. I.P. Natanson, Theory of Functions of a Real Variable. Vol. 1. Frederick Ungar Publishing Co. (1974).
  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.
  30. E.D. Sontag, Comments on integral variants of ISS. Systems Control Lett. 34 (1998) 93-100. [CrossRef] [MathSciNet]
  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.
  32. E.D. Sontag and Y. Wang, Notions of input to output stability. Systems Control Lett. 38 (1999) 235-248. [CrossRef] [MathSciNet]
  33. E.D. Sontag and Y. Wang, Lyapunov characterizations of input to output stability. SIAM J. Control Optim. (to appear).
  34. A.M. Stuart and A.R. Humphries, Dynamical Systems and Numerical Analysis. Cambridge University Press, New York (1996).
  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]
  36. J. Tsinias, A Lyapunov description of stability in control systems. Nonlinear Anal. 13 (1989) 63-74. [CrossRef] [MathSciNet]
  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]
  38. J. Tsinias, N. Kalouptsidis and A. Bacciotti, Lyapunov functions and stability of dynamical polysystems. Math. Systems Theory 19 (1987) 333-354. [CrossRef] [MathSciNet]
  39. V.I. Vorotnikov, Stability and stabilization of motion: Research approaches, results, distinctive characteristics. Avtomat. i Telemekh. (1993) 3-62.
  40. F.W. Wilson, Smoothing derivatives of functions and applications. Trans. Amer. Math. Soc. 139 (1969) 413-428. [CrossRef] [MathSciNet]
  41. T. Yoshizawa, Stability Theory by Lyapunov's Second Method. The Mathematical Society of Japan (1966).
  42. K. Yosida, Functional Analysis, 2nd Edition. Springer Verlag, New York (1968).

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