Brockett's stabilization condition under state constraints

A variant of Brockett's necessary condition for feedback stabilization is derived, in the state constrained case.

[1]  Jean-Michel Coron,et al.  Global asymptotic stabilization for controllable systems without drift , 1992, Math. Control. Signals Syst..

[2]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[3]  J. Zabczyk.  Some comments on stabilizability , 1989 .

[4]  Henry Hermes,et al.  Resonance, stabilizing feedback controls, and regularity of viscosity solutions of Hamilton-Jacobi-Bellman equations , 1996, Math. Control. Signals Syst..

[5]  F. Clarke,et al.  Proximal Smoothness and the Lower{C 2 Property , 1995 .

[6]  Christophe Prieur,et al.  A robust globally asymptotically stabilizing feedback: The example of the artstein’s circles , 2001 .

[7]  K. Brown,et al.  Graduate Texts in Mathematics , 1982 .

[8]  Eduardo Sontag.  Clocks and insensitivity to small measurement errors , 1999 .

[9]  M. A. Krasnoselʹskii,et al.  Geometrical Methods of Nonlinear Analysis , 1984 .

[10]  Eduardo Sontag,et al.  Remarks on continuous feedback , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[11]  R. W. Brockett,et al.  Asymptotic stability and feedback stabilization , 1982 .

[12]  Ludovic Rifford.  Stabilisation des systèmes globalement asymptotiquement commandables , 2000 .

[13]  Eduardo D. Sontag,et al.  Asymptotic controllability implies control feedback stabilization , 1997 .

[14]  Yu. S. Ledyaev,et al.  Nonsmooth analysis and control theory , 1998 .

[15]  F. Ancona,et al.  Patchy Vector Fields and Asymptotic Stabilization , 1999 .

[16]  Yu. S. Ledyaev,et al.  Asymptotic controllability implies feedback stabilization , 1997, IEEE Trans. Autom. Control..

[17]  Melvyn Stuart Berger,et al.  Perspectives in nonlinearity : an introduction to nonlinear analysis , 1968 .

[18]  E. Ryan.  On Brockett's Condition for Smooth Stabilizability and its Necessity in a Context of Nonsmooth Feedback , 1994 .

[19]  Christophe Prieur.  Uniting Local and Global Controllers with Robustness to Vanishing Noise , 2001, Math. Control. Signals Syst..

[20]  Yu. S. Ledyaev,et al.  Asymptotic Stability and Smooth Lyapunov Functions , 1998 .

[21]  Ludovic Rifford,et al.  Existence of Lipschitz and Semiconcave Control-Lyapunov Functions , 2000, SIAM J. Control. Optim..

[22]  板橋 清巳.  Resonance , 1962 .

[23]  Francis H. Clarke,et al.  Feedback Stabilization and Lyapunov Functions , 2000, SIAM J. Control. Optim..

[24]  Eduardo D. Sontag,et al.  Mathematical control theory: deterministic finite dimensional systems (2nd ed.) , 1998 .