@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/} }
TY - JOUR AU - Bacciotti, Andrea AU - Ceragioli, Francesca TI - Stability and stabilization of discontinuous systems and nonsmooth Lyapunov functions JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 1999 SP - 361 EP - 376 VL - 4 PB - EDP-Sciences UR - http://www.numdam.org/item/COCV_1999__4__361_0/ LA - en ID - COCV_1999__4__361_0 ER -
%0 Journal Article %A Bacciotti, Andrea %A Ceragioli, Francesca %T Stability and stabilization of discontinuous systems and nonsmooth Lyapunov functions %J ESAIM: Control, Optimisation and Calculus of Variations %D 1999 %P 361-376 %V 4 %I EDP-Sciences %U http://www.numdam.org/item/COCV_1999__4__361_0/ %G en %F COCV_1999__4__361_0
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] Differential Inclusions, Springer Verlag ( 1984). | MR | Zbl
and ,[2] Prolongations and Stability in Dynamical Systems. Ann. Inst. Fourier (Grenoble) 14 ( 1964) 237-268. | Numdam | MR | Zbl
and ,[3] Local Stabilizability Theory of Nonlinear System, World Scientific ( 1992). | MR
,[4] Liapunov and Lagrange Stability: Inverse Theorems for Discontinuous Systems. Mathematics of Control, Signals and Systems 11 ( 1998) 101-128. | MR | Zbl
and ,[5] Stability Theory of Dynamical Systems, Springer Verlag ( 1970). | MR | Zbl
and ,[6] Optimization and Nonsmooth Analysis, Wiley and Sons ( 1983). | MR | Zbl
,[7] Asymptotic Controllability Implies Feeedback Stabilization. IEEE Trans. Automat. Control 42 ( 1997) 1394-1407. | MR | Zbl
, , and ,[8] Qualitative Properties of Control Systems: A Survey. J. Dynam. Control Systems 1 ( 1995) 1-47. | MR | Zbl
, , and[9] A Relation between Continuous Time-Varying and Discontinuous Feedback Stabilization. J. Math. Systems, Estimation and Control 4 ( 1994) 67-84. | MR | Zbl
and ,[10] Multivalued Differential Equations, de Gruyter ( 1992). | MR | Zbl
[11] Measure Theory and Fine Properties of Functions, CRC ( 1992). | MR | Zbl
and ,[12] Differential Equations with Discontinuous Righthandside, Kluwer Academic Publishers ( 1988). | MR | Zbl
,[13] Backstepping Design with Nonsmooth Nonlinearities, IFAC NOLCOS, Tahoe City, California ( 1995) 483-488.
and ,[14] Controllability and Stability. J. Differential Equations 28 ( 1978) 381-389. | MR | Zbl
and ,[15] Discontinuous Differential Equations. I, II. J. Differential Equations 32 ( 1979) 149-170, 171-185. | MR | Zbl
,[16] On Stabilization of Time-Dependent Affine Control Systems. Rend. Sem. Mat. Univ. Politec. Torino 54 ( 1996) 53-66. | MR | Zbl
and ,[17] Integration, Princeton University Press ( 1947). | MR | Zbl
,[18] 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
and ,[19] An Integral Invariance Principle for Differential Inclusions with Applications in Adaptive Control. SIAM J. Control 36 ( 1998) 960-980. | MR | Zbl
,[20] Lyapunov Stability Theory of Nonsmooth Systems. IEEE Trans. Automat. Control 39 ( 1994) 1910-1914. | MR | Zbl
and ,[21] A Lyapunov-like Characterization of Asymptotic Controllability. SIAM J. Control Optim. 21 ( 1983) 462-471. | MR | Zbl
,[22] Nonsmooth Control Lyapunov Functions, Proc. IEEE Conf. Decision and Control, New Orleans, IEEE Publications ( 1995) 2799-2805.
and ,