Аннотация:We consider the problem of stabilizing a system of ordinary differential equations nonlinear in the state variables with control parameters. Strict pointwise constraints are imposed on the feasible values of the positional control. Assuming sufficient smoothness of the functionson the right-hand side in the differential equations, a piecewise affine system is constructed that approximates the original nonlinear system on a rectangular grid in a given state space domain. The stabilizer can also be found in a piecewise affine form; it corresponds to a continuous but not everywhere differentiable Lyapunov function of a similar structure. The main theorem on sufficient conditions for system stabilizability with the help of piecewise affine control is stated and proved. An algorithm for constructing such a control and a Lyapunov function in a small neighborhood of the zero equilibrium is proposed. An example of numerical solution of the stabilization problem for a specific model system in three-dimensional space is considered.