Abstract
The class of stabilizable nonlinear discrete-time systems is extended in three steps. At the first step, we consider a nonlinear discrete-time system whose elements are bounded from above, the superdiagonal elements are separated from zero, and the elements above them are zeros. The control is supposed to be a scalar state feedback. At this step, the vector of control distribution is the last unit vector. The Lyapunov function is constructed as a positive-definite quadratic form with a constant diagonal matrix. Then, a feedback vector that provides the global stability of the closed-loop system is found.
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