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<p>The robust disturbance attenuation problem for a class of weak nonlinear discrete-time singularly perturbed systems is addressed. By using the fixed-point principle, we first find a sufficient condition to guarantee that the given system is standard. In this case, the original system is decomposed into the continuous-time slow subsystem and discrete-time fast subsystem, respectively. Then, based on the established results for the corresponding slow and fast subsystems, it is shown that the original system is asymptotically stable with a prescribed <i>H</i><sub><i>∞</i></sub> norm bound for sufficiently small values of the perturbation parameter, and the <i>H</i><sub><i>∞</i></sub> performance is still preserved as <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="34_2025_3094_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="44" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varepsilon \to 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ε</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>. For the case where the nominal system is unstable or the desired <i>H</i><sub><i>∞</i></sub> performance cannot be achieved, the problem of designing a control law to make the resulting closed-loop system asymptotically stable with a prescribed <i>H</i><sub><i>∞</i></sub> performance is further addressed. Finally, two numerical examples are given to show the effectiveness of the developed theoretical results.</p>

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Robust Disturbance Attenuation with Stability for Discrete-Time Singularly Perturbed Systems with Nonlinear Disturbances

  • 期刊论文

  • 发表日期：

    2025年4月6日

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  • Wei Liu,
  • Yanyan Wang,
  • Zhiming Wang

摘要

The robust disturbance attenuation problem for a class of weak nonlinear discrete-time singularly perturbed systems is addressed. By using the fixed-point principle, we first find a sufficient condition to guarantee that the given system is standard. In this case, the original system is decomposed into the continuous-time slow subsystem and discrete-time fast subsystem, respectively. Then, based on the established results for the corresponding slow and fast subsystems, it is shown that the original system is asymptotically stable with a prescribed H∞ norm bound for sufficiently small values of the perturbation parameter, and the H∞ performance is still preserved as \(\varepsilon \to 0\) ε → 0 . For the case where the nominal system is unstable or the desired H∞ performance cannot be achieved, the problem of designing a control law to make the resulting closed-loop system asymptotically stable with a prescribed H∞ performance is further addressed. Finally, two numerical examples are given to show the effectiveness of the developed theoretical results.