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Finite-Time Interval Observers’ Design for Switched Systems

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Abstract

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.

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Abbreviations

\(R^n\) :

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., \(A_{ij}>(\ge )0\)

\(E^+\) :

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

\(E^-\) :

\(E^+-E\)

\(||x||_1\) :

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

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Acknowledgements

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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Authors and Affiliations

  1. School of Mechanical and Electrical Engineering, Soochow University, Suzhou, 215131, China

    Xiang Ma, Jun Huang & Liang Chen

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  1. Xiang Ma
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  2. Jun Huang
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Correspondence to Jun Huang.

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Ma, X., Huang, J. & Chen, L. Finite-Time Interval Observers’ Design for Switched Systems. Circuits Syst Signal Process 38, 5304–5322 (2019). https://doi.org/10.1007/s00034-019-01122-0

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  • DOI: https://doi.org/10.1007/s00034-019-01122-0

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