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Well-posedness analysis of switch-driven piecewise affine systems

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1 Author(s)
Imura, J. ; Graduate Sch. of Inf. Sci. & Eng., Tokyo Inst. of Technol., Japan

The well-posedness problem (existence and uniqueness of solutions) of a class of multi-modal piecewise affine systems is addressed, where binary-switches individually act under autonomous switching. First, a new transition rule on the discrete state, called the switch-based transition rule, is introduced and some relations with the mode-based transition rule are discussed. Next, a sufficient condition for such a multi-modal system to be well-posed for all external inputs is derived in terms of well-posedness of its subsystems of lower complexity "bimodal systems". Finally, an easily checkable condition for the bimodal system to be well-posed for all external inputs is given, which consequently allows us to algebraically determine well-posedness of the multi-modal systems in question.

Published in:

Automatic Control, IEEE Transactions on  (Volume:48 ,  Issue: 11 )

Date of Publication:

Nov. 2003

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