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This paper is devoted to the problem of partial asymptotic null-controllability of control systems governed by ordinary differential equations, subjected to possibly mixed state-input constraints. Using Lyapunov functions within the framework of viability theory, feedback controls are designed in such a way a part of system's state can be driven to the origin asymptotically, taking into account the mixed constraints. By using Michael selection theorem, the existence of such controls is proved, in the case of convex constraints, and their expressions are given as continuous selections of an appropriate constructed multifunction. Finally, two examples are processed numerically in order to illustrate the theoretical results.

Partial asymptotic null-controllability with mixed state-input constraints