Circuits, Systems, and Signal Processing

, Volume 38, Issue 4, pp 1561–1582 | Cite as

Integral Sliding Mode Control for Singularly Perturbed Systems with Mismatched Disturbances

  • Chunyu YangEmail author
  • Zhiyuan Che
  • Linna Zhou


This paper presents a novel integral sliding mode control (ISMC) for singularly perturbed systems (SPSs) with mismatched disturbances. A singular perturbation parameter \(\varepsilon \)-dependent disturbance observer is constructed to estimate the disturbances. An ISMC which incorporates the disturbance vector estimate is designed, such that the reachability condition is guaranteed. In order to compensate the effect of mismatched components of the disturbances extracted by the projection matrix theory, \({H_\infty }\) control theory is employed to determine the gain of ISMC by solving a set of linear matrix inequalities. As a result, the closed-loop SPSs under the ISMC are internally exponentially stable with the \({H_\infty }\) performance index guaranteed. Finally, the effectiveness and advantages of the proposed method are demonstrated by two examples.


Singularly perturbed systems (SPSs) Mismatched disturbances Integral sliding mode control (ISMC) Linear matrix inequalities (LMIs) 



This work was supported by the Fundamental Research Funds for the Central Universities (2017XKQY055).


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Information and Control EngineeringChina University of Mining and TechnologyXuzhouPeople’s Republic of China

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