A stability theory for second-order nonsmooth dynamical systems with application to friction problems

Journal des Mathematiques Pures et Appliquees

Volumn 83, Issue 1, 2004, Pages 17-51

  Adly, Samir ^a   Goeleven, Daniel ^b  

^a UNIVERSITY OF LIMOGES   (France)

^b UNIVERSITÉ DE LA RÉUNION   (France)

Author keywords

Convex analysis; Friction problems in Mechanics; LaSalle invariance principle; Lyapunov stability; Nonsmooth Mechanics; Unilateral dynamic systems; Variational inequalities

Indexed keywords

EID: 0347568273     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-7824(03)00071-0     Document Type: Article

References (17)

1. Alvarez J. Orlov I. Acho L. An invariance principle for discontinuous dynamic systems with applications to a Coulomb friction oscillator J. Dynam. Systems 122 2000 687-690
2. B. Brogliato, Absolute stability and the Lagrange-Dirichlet theorem with monotone multivalued mappings, 2002, submitted
3. Brogliato B. On the control of nonsmooth complementarity dynamical systems Philos. Trans. Roy. Soc. Ser. A 359 2001 2369-2384
4. B. Brogliato, Some perspectives on the analysis and control of complementarity systems, IEEE Trans. Automat. Control, 2002, submitted
5. Brogliato B. Nonsmooth Mechanics 2nd Edition 1999 Springer CCES London
6. Goeleven D. Motreanu D. Motreanu V. On the stability of stationary solutions of first-order evolution variational inequalities Adv. Nonlinear Var. Inequal. 6 2003 1-30
7. Goeleven D. Motreanu D. Dumont Y. Rochdi M. Variational and Hemivariational Inequalities, vol. 1: Unilateral Analysis and Mechanics 2003 Kluwer Academic Boston
8. Goeleven D. Motreanu D. Variational and Hemivariational Inequalities, vol. 2: Unilateral Problems 2003 Kluwer Academic Boston
9. D. Goeleven, B. Brogliato, Stability and Unstability Matrices for Linear Evolution Variational Inequalities, 2002, submitted
10. Kato T. Accretive Operators and Nonlinear Evolutions Equations in Banach Spaces, Part 1, Nonlinear Functional Analysis Proc. Sympos. Pure Math. vol. 18 1970 Amer. Math. Society
11. Martins J.A.C. Barbarin S. Raous M. Pinto da Costa A. Dynamic stability of finite linearly elastic systems with unilateral contact and Coulomb friction Comput. Methods Appl. Mech. Engrg. 177 1999 289-328
12. Merkin D.R. Introduction to the Theory of Stability 1996 Springer New York
13. Panagiotopoulos P.D. Inequality Problems in Mechanics and Applications 1985 Birkhäuser Boston
14. Quittner P. On the principle of linearized stability for variational inequalities Math. Ann. 283 1989 257-270
15. Quittner P. An instability criterion for variational inequalities Nonlinear Anal. 15 1990 1167-1180
16. Rouche N. Mawhin J. Equations Différentielles Ordinaires 1973 Masson and Cie Paris Tome 2
17. Showalter R.E. Monotone Operators in Banach Spaces and Nonlinear Partial Differential Equations 1997 Amer. Math. Society Providence, RI