Far Eastern Mathematical Journal

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The strong monotonicity condition for piecewise smooth function on solutions of differental inclusions


Lee Kuh Hwan

2010, issue 2, Ñ. 185–191


Abstract
The condition of decreasing of function on solutions of differential conslusion is studied. Weakened condition in the case of a piecewise smooth function is suggested.

Keywords:
differential inclusion, strong monotonicity, piecewise smooth functions

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References

[1] V. F. Dem'yanov, Minimaks: differenciruemost' po napravleniyam, Izd-vo Leningr. un-ta, L., 1974, 112 s.
[2] V. F. Dem'yanov, L. V. Vasil'ev, Nedifferenciruemaya optimizaciya, Nauka, M., 1981.
[3] A. Bacciotti, F. Ceragioli, “Stability and stabilization of discontinuous systems and nonsmooth Lyapunov functions”, ESAIM: Control, Optimization and Calculus of Variations, 4 (1999), 361–376.
[4] A. Bacciotti, F. Ceragioli, “Nonsmooth Lyapunov functions and discontinuous Caratheodory systems”, Proc. of the 6th IFAC Symposium on Nonlinear Control Systems (NOLCOS 2004), 3, Stuttgart, 2004, 1115–1120.
[5] A. Bacciotti, F. Ceragioli, L. Mazzi, “Differential inclusions and monotonicity conditions for nonsmooth Lyapunov functions”, Set-Valued Analysis, 8 (2000), 299–309.
[6] A. Bacciotti, L. Mazzi, “An invariance principle for nonlinear switched systems”, Systems & Control Letters, 54:11 (2005), 1109–1119.
[7] F. Ceragioli, Discontinuous ordinary defferential equations and stabilization, Tesi di Dottorato di Ricerca in Matematica (PhD Thesis), Universita di Firenze, 2000.
[8] F. H. Clarke, Yu. S. Ledyaev, R. J. Stern, P. R. Wolenski, “Qualitative properties of trajectories of control systems: A survery”, J. Dynam. Contr. Systems, 1:1 (1995), 1–48.
[9] J. Cortes, F. Bullo, “Coordination and geometric optimization via distributed dynamical systems”, SIAM J. Control Optim., 44 (2005), 1543–1574.
[10] Qing Hui, Wassim M. Haddad, Sanjay P. Bhat, “Semistability theory for differential inclusions with applications to consensus problems in dynamical networks with switching topology”, Proc. of the 2008 American Control Conference (Seattle, WA, June), 2008, 3981–3986.
[11] S. Mirica, “Reducing a differential game to a pair of optimal control problems”, Progress in Nonlinear Defferential Equations and Their Applications, 75 (2007), 269–283.
[12] Y. V. Orlov, Discontinuous Systems: Lyapunov Analysis and Robust Synthesis under Uncertainty Conditions, Springer, London, 2008.
[13] E. O. Roxin, “Stability in general control systems”, J. Differential Equations, 1 (1965), 115–150.
[14] V. F. Dem'yanov, “Obobshhenie ponyatiya proizvodnoj”, Sorosovskij obrazovatel'nyj zhurnal, 1996, ¹ 5, 121–127.

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