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Normalised quadratic controls for a class of bilinear systems

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2 Author(s)
Chen, M.-S. ; Dept. of Mech. Eng., Nat. Taiwan Univ., Taipei, Taiwan ; Chen, Y.-Z.

Normalised quadratic control, a modification of the conventional quadratic control method, has recently been proposed to exponentially stabilise a homogeneous bilinear system whose open-loop eigenvalues all fall on the imaginary axis. The normalised quadratic control method is now extended to a broader class of bilinear systems whose open-loop eigenvalues may fall to the left or right of the imaginary axis. It is shown that for bilinear systems that are already open-loop stable, the normalised quadratic control can add to the system an extra exponential decay rate. For open-loop unstable bilinear systems, the normalised quadratic control can stabilise the system if the extra exponential decay rate provided by the control is larger than the open-loop system's growth rate.

Published in:

Control Theory and Applications, IEE Proceedings -  (Volume:149 ,  Issue: 6 )