Circuits, Systems, and Signal Processing

, Volume 38, Issue 11, pp 5304–5322 | Cite as

Finite-Time Interval Observers’ Design for Switched Systems

  • Xiang Ma
  • Jun HuangEmail author
  • Liang Chen
Short Paper


In this study, a finite-time interval observers’ design method is developed for switched systems suffering from disturbance. First, the interval observer frames for the systems are constructed. Then, sufficient conditions are derived to guarantee that the upper and lower error systems are both positive and finite-time bound. Unlike the current studies, all the conditions proposed in this paper are formulated in the form of linear programming. Finally, two numerical examples are provided to show the efficiency of designed observers.


Interval observers Finite-time boundedness Switched systems Linear programming 

List of Symbols


n-dimensional Euclidean space

\(R^{n\times m}\)

The set of \(n{\times }m\) real matrices

\(x>(\ge )0\)

Its components are positive (nonnegative), i.e., \(x_{i}>(\ge )0\)

\(A>(\ge )0\)

Its components are positive (nonnegative), i.e., \(A_{ij}>(\ge )0\)


\(\max \{E,0\}\)




The 1-norm of the vector x

\(\overline{\lambda }(v)\)

The maximum value of the elements of the vector v

\(\underline{\lambda }(v)\)

The minimum value of the elements of the vector v

\(\mathbf 1 _n\)

The vector whose entries equal to 1



This work is supported by National Natural Science Foundation of China (61403267), Natural Science Foundation of Jiangsu Province (BK20130322), and China Postdoctoral Science Foundation (2017M611903).


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical and Electrical EngineeringSoochow UniversitySuzhouChina

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