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Flow stability of patchy vector fields and robust feedback stabilization. (English) Zbl 1055.34094
A class of discontinuous, piecewise smooth vector fields is considered. The stability of a patchy vector field is defined and detailed discussed. Using methods taken from the theory of vector fields, sufficient conditions for uniform stability are formulated and proved. Next, patchy vector fields with impulsive perturbations are discussed. Stabilizing discontinuous feedback controls that have robustness properties with respect to external disturbances are constructed and analyzed. Moreover, the paper contains many remarks and comments on the feedback stabilization problems for continuous-time control systems. Finally, it should be pointed out that similar feedback stabilization poblems have been presented in the paper [F. Ancona and A. Bressan, ESAIM, Control Optim. Calc. Var. 4, 445–471 (1999; Zbl 0924.34058)].

MSC:
34D20 Stability of solutions to ordinary differential equations
93D15 Stabilization of systems by feedback
93D21 Adaptive or robust stabilization
34A36 Discontinuous ordinary differential equations
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