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Global Controllability of Switched Affine Systems

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Emergent Problems in Nonlinear Systems and Control

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 393))

Introduction

Consider a linear control system

$$ \dot{x}=Ax+\sum_{i=1}^mb_iu_i:=Ax+Bu,\quad x\in {\mathbb R}^n,\;u\in {\mathcal U}^m, (9.1) $$

where \({\mathcal U}\) is the set of piecewise continuous functions. It is well known that (9.1) is controllable, iff the controllability matrix

$$ {\mathcal C}=\begin{bmatrix}B&AB&\cdots&A^{n-1}B\end{bmatrix} (9.2) $$

has full row rank, i.e., \(rank({\mathcal C})=n\) [12].

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Author information

Authors and Affiliations

  1. Institute of Systems Science, Chinese Academy of Sciences, Beijing, 100080, P.R. China

    Daizhan Cheng

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  1. Daizhan Cheng
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics and Statistics, Center for BioCybernetics and Intelligent Systems, Texas Tech University, Broadway and Boston, 79409-1042, Lubbock, TX, USA

    Bijoy K. Ghosh

  2. Dept. of Mathematics and Statistics, Texas Tech University, Broadway and Boston, 79409-1042, Lubbock, TX, USA

    Clyde F. Martin

  3. Dept. of Mathematics, Stockholm University, SE-106 91, Stockholm, Sweden

    Yishao Zhou

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Cheng, D. (2009). Global Controllability of Switched Affine Systems. In: Ghosh, B.K., Martin, C.F., Zhou, Y. (eds) Emergent Problems in Nonlinear Systems and Control. Lecture Notes in Control and Information Sciences, vol 393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03627-9_9

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  • DOI: https://doi.org/10.1007/978-3-642-03627-9_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03626-2

  • Online ISBN: 978-3-642-03627-9

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