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A generalization of Conventional Matrix Product (CMP), called the
Semi-Tensor Product (STP), is proposed. It extends the CMP to two
arbitrary matrices and maintains all fundamental properties of CMP.
In addition, it has a pseudo-commutative property, which makes it
more superior to CMP. The STP was proposed by the authors to deal
with higher-dimensional data as well as multilinear mappings. After
over a decade of development, STP has been proven to be a powerful
tool in dealing with nonlinear and logical calculations. This book
is a comprehensive introduction to the theory of STP and its
various applications, including logical function, fuzzy control,
Boolean networks, analysis and control of nonlinear systems,
amongst others.
Analysis and Control of Boolean Networks presents a systematic new
approach to the investigation of Boolean control networks. The
fundamental tool in this approach is a novel matrix product called
the semi-tensor product (STP). Using the STP, a logical function
can be expressed as a conventional discrete-time linear system. In
the light of this linear expression, certain major issues
concerning Boolean network topology - fixed points, cycles,
transient times and basins of attractors - can be easily revealed
by a set of formulae. This framework renders the state-space
approach to dynamic control systems applicable to Boolean control
networks. The bilinear-systemic representation of a Boolean control
network makes it possible to investigate basic control problems
including controllability, observability, stabilization,
disturbance decoupling etc.
Analysis and Control of Boolean Networks presents a systematic new
approach to the investigation of Boolean control networks. The
fundamental tool in this approach is a novel matrix product called
the semi-tensor product (STP). Using the STP, a logical function
can be expressed as a conventional discrete-time linear system. In
the light of this linear expression, certain major issues
concerning Boolean network topology - fixed points, cycles,
transient times and basins of attractors - can be easily revealed
by a set of formulae. This framework renders the state-space
approach to dynamic control systems applicable to Boolean control
networks. The bilinear-systemic representation of a Boolean control
network makes it possible to investigate basic control problems
including controllability, observability, stabilization,
disturbance decoupling etc.
From Dimension-Free Matrix Theory to Cross-Dimensional Dynamic
Systems illuminates the underlying mathematics of semi-tensor
product (STP), a generalized matrix product that extends the
conventional matrix product to two matrices of arbitrary
dimensions. Dimension-varying systems feature prominently across
many disciplines, and through innovative applications its newly
developed theory can revolutionize large data systems such as
genomics and biosystems, deep learning, IT, and information-based
engineering applications.
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