Tensor-Product Representation for Switched Linear Systems

Dengyin Jiang, Lisheng Hu^*

Department of Automation, Shanghai Jiao Tong University, Shanghai, China.

DOI: 10.4236/jamp.2015.33045                

Abstract

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.

Keywords

Switched Linear Systems, Tensor-Product Representation, Stability

Conflicts of Interest

The authors declare no conflicts of interest.

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