Weighted inline image control with inline image-stability constraint for switched positive linear systems

Authors

  • Yanhui Tong,

    1. Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, China
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  • Lixian Zhang,

    1. Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, China
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  • Michael Basin,

    1. Department of Physical and Mathematical Sciences, Autonomous University of Nuevo Leon, San Nicolas de los Garza, Nuevo Leon, Mexico
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  • Changhong Wang

    Corresponding author
    1. Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, China
    • Correspondence to: Changhong Wang, Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin, 150080, China.

      E-mail: cwang@hit.edu.c

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SUMMARY

This paper is concerned with the problem of inline image control with inline image-stability constraint for a class of switched positive linear systems. The inline image-stability means that all the poles of each subsystem of the resultant closed-loop system belong to a prescribed disk in the complex plane. A sufficient condition is derived for the existence of a set of state-feedback controllers, which guarantees that the closed-loop system is not only positive and exponentially stable with each subsystem inline image-stable but also has a weighted inline image performance for a class of switching signals with average dwell time greater than a certain positive constant. Both continuous-time and discrete-time cases are considered, and all of the obtained conditions are formulated in terms of linear matrix inequalities, whose solution also yields the desired controller gains and the corresponding minimal average dwell time. Numerical examples are given to illustrate the effectiveness of the presented approach.Copyright © 2012 John Wiley & Sons, Ltd.

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