By Zhanshan Wang, Zhenwei Liu, Chengde Zheng
This e-book makes a speciality of the soundness of the dynamical neural approach, synchronization of the coupling neural method and their functions in automation regulate and electric engineering. The redefined proposal of balance, synchronization and consensus are followed to supply a greater clarification of the complicated neural community. Researchers within the fields of dynamical structures, machine technological know-how, electric engineering and arithmetic will enjoy the discussions on advanced structures. The ebook also will aid readers to higher comprehend the idea at the back of the regulate procedure and its design.
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Example text
In some cases of network parameters, Hopfield neural networks are a special case of Cohen–Grossberg neural networks. For the case of strictly positive amplification, stability analysis of Cohen–Grossberg neural networks is along the same routine as that of Hopfield neural networks. In this case, the equilibrium point of recurrent neural networks can be positive, negative, zero, or their mixtures. However, for the case of nonnegative amplification, stability analysis of Cohen–Grossberg neural networks is a different routine from that of Hopfield neural networks, and the equilibrium point must be nonnegative, which represents the survival and extinction of species.
6) proposed in Cohen and Grossberg [59] includes both the Additive Model and Shunting Model, among others. A year later, Hopfield [29] published the special case of the Additive Model and Lyapunov function and asserted, without proof, that trajectories approach equilibria. Based on this 1984 article, the Additive Model has been erroneously called the Hopfield network by a number of investigators, despite the fact that it was published in multiple articles since the 1960s and its Lyapunov function was also published in 1982–1983.
For the classical control theory, for example, transfer function methods, it can be converted into Hinfinity problem using the H-infinity norm and realization theory. Therefore, in some cases and for some specific problems, LMI method can also be applied to classical control theory. That is, both modern control system theory and classical control theory can make a space for LMI method. (4) Technically, many matrix theory methods can be incorporated into the LMIbased methods. Therefore, like algebraic inequality methods (which mainly deal with the scalar space or dot measure, and almost all scalar inequalities can be used in the algebraic inequality methods), many matrix inequalities can be used in the LMI-based method and many kinds of LMI-based stability results can be presented.