<p>This paper addresses the feedback stabilization for a class of nonlinear discrete-time systems with delays. Two kinds of stabilization will be investigated based on an inequality parameterized by <i>r</i>. First, for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(r =2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>r</mi> <mo>=</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, sufficient conditions for exponential stabilization are provided. Next, for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(r &gt; 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>r</mi> <mo>&gt;</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>, strong stabilization is attained with the following explicit polynomial decay rate: <Equation ID="Equ32"> <EquationSource Format="TEX">\(\begin{aligned} \Vert x(k) \Vert =\mathcal {O}\left( k^{-\frac{1}{2(r-1)}}\right) , \hspace{0.2cm} \text {as} \hspace{0.2cm} k\rightarrow +\infty . \end{aligned}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mtable> <mtr> <mtd columnalign="right"> <mrow> <mrow> <mo stretchy="false">‖</mo> <mi>x</mi> <mrow> <mo stretchy="false">(</mo> <mi>k</mi> <mo stretchy="false">)</mo> </mrow> <mo stretchy="false">‖</mo> </mrow> <mo>=</mo> <mi mathvariant="script">O</mi> <mfenced close=")" open="("> <msup> <mi>k</mi> <mrow> <mo>-</mo> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mo stretchy="false">(</mo> <mi>r</mi> <mo>-</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </msup> </mfenced> <mo>,</mo> <mspace width="5.69046pt" /> <mtext>as</mtext> <mspace width="5.69046pt" /> <mi>k</mi> <mo stretchy="false">→</mo> <mo>+</mo> <mi>∞</mi> <mo>.</mo> </mrow> </mtd> </mtr> </mtable> </mrow> </math></EquationSource> </Equation>Additionally, weak stabilization and partial strong stabilization have been discussed. Finally, numerical examples and simulations are provided to illustrate the theoretical obtained results.</p>