Properties And Applications Of Semi-tensor Product Of Matrices

Semi-tensor product of matrices is a new matrix multiplication,proposed by Professor Cheng daizhan.Given two matrices,A ∈ Mm×n,B ∈ Mm×n,the semi-tensor product of matrices A and B is defined as Aa B:=(A(?)It/n)(B(?)It/p)where the t=lcm{n,p} denotes the least common multiple of n and p.The semi tensor product of matrices not only overcomes the requirement of matrix dimension in common matrix multiplication,but also preserves almost all properties of common matrix multiplication.Therefore,it can also be regarded as a generalization of common matrix multiplication.Based on the introduction of the definition and main properties of matrix semi tensor product,this paper discusses the application of matrix semi tensor product in the observability of mixed valued logic control networkIn Chapter 1,the background and significance of matrix semi tensor product,the research status of matrix semi tensor product,the overview of logic control network,the research problems and results of this paper are introduced.In Chapter 2,the definition and properties of matrix semi tensor product and the method of logic operator semi tensor product are introduced,that is,using the semi tensor product of matrix to express logic operator in the form of matrix and vector.In Chapter 3,we first transform the semi tensor product of transfer matrix of mixed valued logic control network into algebraic expression.Then,combined with the definition of observability of Boolean control network,four definitions of observability of mixed valued logic control network are given.At last,every observability is discussed and the corresponding theorem is given.Chapter 4 makes a brief summary of this paper.