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All issues Volume 29 (2023) ESAIM: COCV, 29 (2023) 84 References
Open Access
Issue
ESAIM: COCV
Volume 29, 2023
Article Number 84
Number of page(s) 42
DOI https://doi.org/10.1051/cocv/2023074
Published online 17 November 2023
  1. V. Acary and B. Brogliato, Numerical Methods for Nonsmooth Dynamical Systems. Lecture Notes in Applied and Computational Mechanics. Springer-Verlag Berlin Heidelberg (2008) xxi+525. [Google Scholar]
  2. S. Adly, H. Attouch and A. Cabot, Finite time stabilization of nonlinear oscillators subject to dry friction. Nonsmooth Mechanics and Analysis. Adv. Mech. Math., Vol. 12, Springer, New York (2006) 289–304. [CrossRef] [Google Scholar]
  3. S. Adly, A Variational Approach to Nonsmooth Dynamics: Applications in Unilateral Mechanics and Electronics. Springer Briefs in Mathematics (2017) xv+159. [Google Scholar]
  4. R. Agarwal and V. Lakshmikantham, Uniqueness and Nonuniqueness Criteria for Ordinary Differential Equations. WorldScientific (1993) 324. [Google Scholar]
  5. H.H. Bauschke and P.L. Combettes, Convex Analysis and Monotone Operator Theory in Hilbert Spaces. Springer, New York (2011) xvi+468. [Google Scholar]
  6. S.P. Bhat and D.S. Bernstein, Lyapunov analysis of finite-time differential equations, in Proceedings of the American Control Conference. IEEE, Washington, USA (1995) 1831–1832. [Google Scholar]
  7. S.P. Bhat and D.S. Bernstein, Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38 (2000) 751–766. [CrossRef] [MathSciNet] [Google Scholar]
  8. F.J. Bejarano and L.M. Fridman, High order sliding mode observer for linear systems with unbounded unknown inputs. Int. J. Control. 9 (2010) 1920–1929. [CrossRef] [Google Scholar]
  9. T. Bonnesen and W. Fenchel, Theory of convex Bodies. Translated from the German and edited by L. Boron, C. Christenson and B. Smith. BCS Associates (1987) x+172. [Google Scholar]
  10. H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer-Verlag, New York (2011) xiv+600. [Google Scholar]
  11. B. Brogliato, Nonsmooth Mechanics: Models, Dynamics and Control. 3rd edn. Springer (2016). [CrossRef] [Google Scholar]
  12. A. Cabot, Stabilization of oscillators subject to dry friction: finite time convergence versus exponential decay results. Trans. Am. Math. Soc. 360 (2008) 103–121. [CrossRef] [Google Scholar]
  13. F. Chernousko, I. Ananievskii and S. Reshmin, Control of Nonlinear Dynamical Systems: Methods and Applications. Springer-Verlag (2008) xii+396. [Google Scholar]
  14. G. Colombo, P. Gidoni and E. Vilches, Stabilization of periodic sweeping processes and asymptotic average velocity for soft locomotors with dry friction. Discrete Contin. Dyn. Syst. Ser. A 42 (2022) 737–757. [CrossRef] [Google Scholar]
  15. F. Dinuzzo and A. Ferrara, Higher order sliding mode controllers with optimal reaching. IEEE Trans. Automat. Contr. 54 (2009) 2126–2136. [CrossRef] [Google Scholar]
  16. H. Du, C. Qian, S. Yang and S. Li, Recursive design of finite-time convergent observers for a class of time-varying nonlinear systems. Automatica 49 (2013) 601–609. [CrossRef] [MathSciNet] [Google Scholar]
  17. C.O. Frederick and P.J. Armstrong, Convergent internal stresses and steady cyclic states of stress. J. Strain Anal. 1 (1966) 154–159. [CrossRef] [Google Scholar]
  18. A. Filippov, Differential Equations with Discontinuous Right-hand Sides. Springer Dordrecht, ser. Mathematics and Its Applications (Soviet Series) (1988) x+304. [Google Scholar]
  19. P. Gidoni, Rate-independent soft crawlers. Q. J. Mech. Appl. Math. 71 (2018) 369–409. [Google Scholar]
  20. B. Grünbaum, Convex Polytopes. 2nd edn. Graduate Texts in Mathematics, 221. Springer-Verlag, New York (2003) xvi+468. [Google Scholar]
  21. I. Gudoshnikov and O. Makarenkov, Stabilization of the response of cyclically loaded lattice spring models with plasticity. ESAIM: COCV 27 (2021) S8. [CrossRef] [EDP Sciences] [Google Scholar]
  22. I. Gudoshnikov and O. Makarenkov, Structurally stable families of periodic solutions in sweeping processes of networks of elastoplastic springs. Phys. D 406 (2020) 132443. [CrossRef] [MathSciNet] [Google Scholar]
  23. I. Gudoshnikov, Y. Jiao, O. Makarenkov and D. Chen, Sweeping Process Approach to Stress Analysis in Elastoplastic Lattice Springs Models with Applications to Hyperuniform Network Materials. (2022) submitted, preprint available at arXiv:2204.03015. [Google Scholar]
  24. I. Gudoshnikov, O. Makarenkov and D. Rachinskiy, Finite-time stability of polyhedral sweeping processes with application to elastoplastic systems. SIAM J. Control Optim. 60 (2022) 1320–1346. [CrossRef] [MathSciNet] [Google Scholar]
  25. W.M. Haddad and A. L’Afflitto, Finite-Time Stabilization and Optimal Feedback Control. IEEE Trans. Automat. Contr. 61 (2016) 1069–1074. [CrossRef] [Google Scholar]
  26. W. Han and B.D. Reddy, Plasticity. Mathematical Theory and Numerical Analysis. 2nd edn. Interdisciplinary Applied Mathematics, 9. Springer, New York (2013). [Google Scholar]
  27. W.P.M.H. Heemels, J.M. Schumacher and S. Weiland, Linear complementarity systems. SIAM J. Appl. Math. 60 (2000) 1234–1269. [CrossRef] [MathSciNet] [Google Scholar]
  28. J.B. Hiriart-Urruty and C. Lemaréchal, Fundamentals of Convex Analysis. Grundlehren Text Editions, Springer-Verlag, Berlin (2001) x+259. [Google Scholar]
  29. Y. Hong, Finite-time stabilization and stabilizability of a class of controllable systems. Syst. Control Lett. 46 (2002) 231–236. [CrossRef] [Google Scholar]
  30. Y. Hong, J. Wang and D. Cheng, Adaptive finite-time control of nonlinear systems with parametric uncertainty. IEEE Trans. Automat. Contr. 51 (2006) 858–862. [CrossRef] [Google Scholar]
  31. P. Krejčí, Hysteresis, Convexity and Dissipation in Hyperbolic Equations. GAKUTO International Series. Mathematical Sciences and Applications, 8. Gakkōtosho Co. Ltd., Tokyo (1996) viii+211. [Google Scholar]
  32. M. Kunze and M.D.M. Marques, An introduction to Moreau’s sweeping process, in Impacts in Mechanical Systems. Lecture Notes in Physics, edited by Brogliato, Vol. 551. Springer, Berlin, Heidelberg (2000). [CrossRef] [Google Scholar]
  33. J. Matoušek and B. Gärtner, Understanding and Using Linear Programming. Berlin, Springer (2007) viii+226. [Google Scholar]
  34. B. Mordukhovich, Variational Analysis and Applications. Springer Monographs in Mathematics. Springer Cham (2018) xix+622. [Google Scholar]
  35. J.-J. Moreau, On Unilateral Constraints, Friction and Plasticity. New Variational Techniques in Mathematical Physics (Centro Internaz. Mat. Estivo (C.I.M.E.), II Ciclo, Bressanone, 1973). Edizioni Cremonese, Rome (1974) 171–322. [Google Scholar]
  36. J.-J. Moreau, Application of convex analysis to the treatment of elastoplastic systems, in Applications of Methods of Functional Analysis to Problems in Mechanics: Joint Symposium IUTAM/IMU held in Marseille, September 1–6, 1975, edited by P. Germain and B. Nayroles. Springer (1976) 56–89. [Google Scholar]
  37. J.-J. Moreau, Numerical aspects of the sweeping process. Comput. Methods Appl. Mech. Eng. 177 (1999) 329–349. [CrossRef] [Google Scholar]
  38. J.-J. Moreau, An introduction to unilateral dynamics, in Novel Approaches in Civil Engineering. Lecture Notes in Applied and Computational Mechanics, edited by M. Frémond and F. Maceri, Vol. 14. Springer, Berlin, Heidelberg (2004). [Google Scholar]
  39. J. Nocedal and S.J. Wright, Numerical optimization. 2nd edn. Springer Series in Operations Research and Financial Engineering. Springer, New York, NY, (2006) xxii+664. [Google Scholar]
  40. H. Pan, W. Sun and H. Gao, Finite-time vibration control for active suspension systems, in Vibration Control and Actuation of Large-Scale Systems, Emerging Methodologies and Applications in Modelling. Academic Press (2020) 185–223. [Google Scholar]
  41. C. Qian and W. Lin, Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Syst. Control. Lett. 42 (2001) 185–200. [CrossRef] [Google Scholar]
  42. R.T. Rockafellar, Convex Analysis. Princeton Mathematical Series, No. 28. Princeton University Press, Princeton, NJ (1970) xviii+451. [Google Scholar]
  43. A. Schrijver, Theory of Linear and Integer Programming. Wiley-Interscience Series in Discrete Mathematics. John Wiley & Sons Ltd. (1987) 484. [Google Scholar]
  44. S. Seo, H. Shim and J.H. Seo, Global finite-time stabilization of a nonlinear system using dynamic exponent scaling. 47th IEEE Conference, Decision and Control, Cancun, Mexico, Dec. 9–11 (2008) 3805–3810. [Google Scholar]
  45. A. Shapiro, Differentiability properties of metric projections onto convex sets. J. Optim. Theory Appl. 169 (2016) 953–964. [CrossRef] [MathSciNet] [Google Scholar]
  46. V. Utkin, J. Guldner and J. Shi, Sliding Mode Control in Electro-mechanical Systems. CRC Press (2009) 503. [Google Scholar]
  47. S.T. Venkataraman and S. Gulati, Terminal sliding modes: a new approach to nonlinear control systems. Proc. 5th Int. Conf. Advanced Robotics, Pisa, Italy (1991) 443–448. [Google Scholar]
  48. S. Yua, X. Yub, B. Shirinzadehc and Z. Mand, Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatica 41 (2005) 1957–1964. [Google Scholar]
  49. X. Zhang, G. Feng and Y. Sun, Finite-time stabilization by state feedback control for a class of time-varying nonlinear systems. Automatica 48 (2012) 499–504. [CrossRef] [MathSciNet] [Google Scholar]

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