Semi-tensor product (STP) of matrices has attracted more and more attention from both control theory and engineering in the last two decades. This paper presents a comprehensive survey on the applications of STP method in engineering. Firstly, some preliminary results on STP method are recalled. Secondly, some applications of STP method in engineering, including gene regulation, power system, wireless communication, smart grid, information security, combustion engine and vehicle control, are reviewed. Finally, some potential applications of STP method are predicted.

A survey on applications of semi-tensor product method in engineering

Finite-time stability analysis of stochastic switched boolean networks with impulsive effect

This paper devotes to establishing a bridge between asymptotical stability of a probabilistic Boolean network (PBN) and a solution to its induced equations, which are induced from the PBN's transition matrix. By utilizing the semitensor product technique routinely, the dynamics of a PBN with coincident state delays can be equivalently converted into that of a higher dimensional PBN without delays. Subsequently, several novel stability criteria are derived from the standpoint of equations’ solution. The most significant finding is that a PBN is globally asymptotically stable at a predesignated one-point distribution if and only if a vector, obtained by adding 1 at the bottom of this distribution, is the unique nonnegative solution to PBN's induced equations. Moreover, the influence of coincident state delays on PBN's asymptotical stability is explicitly analyzed without consideration of the convergence rate. Consequently, such bounded state delays are verified to have no impact on PBN's stability, albeit delays are time-varying. Based on this worthwhile observation, the time computational complexity of the aforementioned approach can be reduced by removing delays directly. Furthermore, this universal procedure is summarized to reduce the time complexity of some previous results in the literature to a certain extent. Two examples are employed to demonstrate the feasibility and effectiveness of the obtained theoretical results.

Asymptotical Stability of Probabilistic Boolean Networks With State Delays

This article studies the stability in probability of probabilistic Boolean networks and stabilization in the probability of probabilistic Boolean control networks. To simulate more realistic cellular systems, the probability of stability/stabilization is not required to be a strict one. In this situation, the target state is indefinite to have a probability of transferring to itself. Thus, it is a challenging extension of the traditional probability-one problem, in which the self-transfer probability of the target state must be one. Some necessary and sufficient conditions are proposed via the semitensor product of matrices. Illustrative examples are also given to show the effectiveness of the derived results.

Stability and Stabilization in Probability of Probabilistic Boolean Networks

On the ensemble controllability of Boolean control networks using STP method

This paper investigates the Lyapunov-based stability analysis and the construction of Lyapunov functions for Boolean networks (BNs) and establishes a new framework of Lyapunov theory for BNs via the semitensor product of matrices. First, we study how to define a Lyapunov function for BNs. A proper form of pseudo-Boolean functions is found, and the concept of (strict-) Lyapunov functions is thus given. It is shown that a pseudo-Boolean function in the proper form can play the role of Lyapunov functions for BNs, based on which several Lyapunov-based stability results are obtained. Second, we study how to construct a Lyapunov function for BNs and propose two methods for this problem: one is a definition-based method, and the other is a structure-based one. Third, the existence of strict-Lyapunov functions is studied, and a converse Lyapunov theorem as well as a necessary and sufficient condition are obtained for the asymptotical stability. Finally, as an application, the obtained results are applied to the s...

Haitao Li

Papers

Lyapunov-Based Stability and Construction of Lyapunov Functions for Boolean Networks