This
paper presents the method for the construction of tensor-product representation
for multivariate switched linear systems, based on a suitable tensor-product
representation of vectors and matrices. We obtain a representation theorem for
multivariate switched linear systems. The stability properties of the
tensor-product representation are investigated in depth, achieving the
important result that any stable switched systems can be constructed a stable
tensor-product representation of finite dimension. It is shown that the
tensor-product representation provides a high level framework for describing
the dynamic behavior. The interpretation of expressions within the
tensor-product representation framework leads to enhanced conceptual and
physical understanding of switched linear systems dynamic behavior.
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