Multistability of Switched Neural Networks with Piecewise Linear Activation Functions under State-Dependent Switching

Zhenyuan Guo, Linlin Liu, Jun Wang

Research output: Contribution to journalArticlepeer-review

29 Citations (Scopus)


This paper is concerned with the multistability of switched neural networks with piecewise linear activation functions under state-dependent switching. Under some reasonable assumptions on the switching threshold and activation functions, by using the state-space decomposition method, contraction mapping theorem, and strictly diagonally dominant matrix theory, we can characterize the number of equilibria as well as analyze the stability/instability of the equilibria. More interesting, we can find that the switching threshold plays an important role for stable equilibria in the unsaturation regions of activation functions, and the number of stable equilibria of an n -neuron switched neural network with state-dependent parameters increases to 3n from 2n in the conventional one. Furthermore, for two-neuron switched neural networks, the precise attraction basin of each stable equilibrium point can be figured out, and its boundary is composed of the stable manifolds of unstable equilibrium points and the switching lines. Two simulation examples are discussed in detail to substantiate the effectiveness of the theoretical analysis.

Original languageEnglish
Article number8532132
Pages (from-to)2052-2066
Number of pages15
JournalIEEE Transactions on Neural Networks and Learning Systems
Issue number7
Publication statusPublished - Jul 2019
Externally publishedYes


  • Exponential stability
  • multistability
  • piecewise linear activation functions
  • state dependent
  • switched neural network


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