Stability and stabilization of discontinuous systems and nonsmooth Lyapunov functions
ESAIM: Control, Optimisation and Calculus of Variations, Tome 4 (1999), pp. 361-376.
@article{COCV_1999__4__361_0,
     author = {Bacciotti, Andrea and Ceragioli, Francesca},
     title = {Stability and stabilization of discontinuous systems and nonsmooth {Lyapunov} functions},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {361--376},
     publisher = {EDP-Sciences},
     volume = {4},
     year = {1999},
     mrnumber = {1693045},
     zbl = {0927.34034},
     language = {en},
     url = {http://www.numdam.org/item/COCV_1999__4__361_0/}
}
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Bacciotti, Andrea; Ceragioli, Francesca. Stability and stabilization of discontinuous systems and nonsmooth Lyapunov functions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 4 (1999), pp. 361-376. http://www.numdam.org/item/COCV_1999__4__361_0/

[1] J.P. Aubin and A. Cellina, Differential Inclusions, Springer Verlag ( 1984). | MR | Zbl

[2] J. Auslander and P. Seibert, Prolongations and Stability in Dynamical Systems. Ann. Inst. Fourier (Grenoble) 14 ( 1964) 237-268. | Numdam | MR | Zbl

[3] A. Bacciotti, Local Stabilizability Theory of Nonlinear System, World Scientific ( 1992). | MR

[4] A. Bacciotti and L. Rosier, Liapunov and Lagrange Stability: Inverse Theorems for Discontinuous Systems. Mathematics of Control, Signals and Systems 11 ( 1998) 101-128. | MR | Zbl

[5] N.P. Bhatia and G.P. Szëgo, Stability Theory of Dynamical Systems, Springer Verlag ( 1970). | MR | Zbl

[6] F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley and Sons ( 1983). | MR | Zbl

[7] F.H. Clarke, Yu.S. Ledyaev, E.D. Sontag and A.I. Subbotin, Asymptotic Controllability Implies Feeedback Stabilization. IEEE Trans. Automat. Control 42 ( 1997) 1394-1407. | MR | Zbl

[8] F.H. Clarke, Yu.S. Ledyaev, R.J. Stern and P.R. Wolenski Qualitative Properties of Control Systems: A Survey. J. Dynam. Control Systems 1 ( 1995) 1-47. | MR | Zbl

[9] J.M. Coron and L. Rosier, A Relation between Continuous Time-Varying and Discontinuous Feedback Stabilization. J. Math. Systems, Estimation and Control 4 ( 1994) 67-84. | MR | Zbl

[10] K. Deimling Multivalued Differential Equations, de Gruyter ( 1992). | MR | Zbl

[11] L.C. Evans and R.F. Gariepy, Measure Theory and Fine Properties of Functions, CRC ( 1992). | MR | Zbl

[12] A.F. Filippov, Differential Equations with Discontinuous Righthandside, Kluwer Academic Publishers ( 1988). | MR | Zbl

[13] R.A. Freeman and P.V. Kokotovic, Backstepping Design with Nonsmooth Nonlinearities, IFAC NOLCOS, Tahoe City, California ( 1995) 483-488.

[14] V. Jurdjevic and J.P. Quinn, Controllability and Stability. J. Differential Equations 28 ( 1978) 381-389. | MR | Zbl

[15] O. Hájek, Discontinuous Differential Equations. I, II. J. Differential Equations 32 ( 1979) 149-170, 171-185. | MR | Zbl

[16] L. Mazzi and V. Tabasso, On Stabilization of Time-Dependent Affine Control Systems. Rend. Sem. Mat. Univ. Politec. Torino 54 ( 1996) 53-66. | MR | Zbl

[17] E.J. Mcshane, Integration, Princeton University Press ( 1947). | MR | Zbl

[18] B. Paden and S. Sastry, A Calculus for Computing Filippov's Differential Inclusion with Application to the Variable Structure Control of Robot Manipulators. IEEE Trans. Circuits and Systems Cas-34 ( 1997) 73-81. | MR | Zbl

[19] E.P. Ryan, An Integral Invariance Principle for Differential Inclusions with Applications in Adaptive Control. SIAM J. Control 36 ( 1998) 960-980. | MR | Zbl

[20] D. Shevitz and B. Paden, Lyapunov Stability Theory of Nonsmooth Systems. IEEE Trans. Automat. Control 39 ( 1994) 1910-1914. | MR | Zbl

[21] E.D. Sontag, A Lyapunov-like Characterization of Asymptotic Controllability. SIAM J. Control Optim. 21 ( 1983) 462-471. | MR | Zbl

[22] E.D. Sontag and H. Sussmann, Nonsmooth Control Lyapunov Functions, Proc. IEEE Conf. Decision and Control, New Orleans, IEEE Publications ( 1995) 2799-2805.