Performance analysis for multi-valued logical networks

In this paper, the performance in the form of weighted l1-gain for k-valued logical control networks are defined and discussed via semi-tensor product method. First, the input energy and output energy can be described by the definition and construction of pseudo-logical functions. Along this line, the weighted l1-gain is introduced. In order to ensure that a k-valued logical control network is internally asymptotically stable and has an l1-gain no more than a given scalar, a sufficient condition is established by extending several Lyapunov results of Boolean networks to those of k-valued logical networks. Finally, an illustrative example is given to show the feasibility of the theoretical results.