摘要：AbstractWe consider a discrete nonlinear control time-varying systemx(k+ 1) =f(k, x(k), u(k)), k∈ ℕ,x∈ ℝn,u∈ ℝr. A control process of this system is a pair(x(k), u(k))k ∈ N consisting of a control(u(k))k∈Nand some solution(x(k))k∈Nof the system with this control. We assume that the control process is defined for allk∈ N. We have obtained sufficient conditions for uniform and non-uniform (with respect to the initial moment) exponential stabilization of the control process with any pregiven decay of rate. Exponential convergence to zero of the deviation of both the state vector and the control vector is guaranteed. The result is based on the property of uniform complete controllability (in the sense of Kalman) for a system of linear approximation.
