Stability Analysis of Continuous-Time Recurrent Neural Networks by IQC with Copositive Multipliers

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  • Takao Ryota
    Graduate School of Information Science and Electrical Engineering, Kyushu University
  • Fujii Tatsuki
    Graduate School of Information Science and Electrical Engineering, Kyushu University
  • Motooka Hayato
    Graduate School of Information Science and Electrical Engineering, Kyushu University
  • Ebihara Yoshio
    Graduate School of Information Science and Electrical Engineering, Kyushu University

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Other Title
  • 積分二次制約と共正値マルチプライアを用いた連続時間再帰型ニューラルネットワークの安定性解析

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<p>This paper addresses the stability analysis problem of recurrent neural networks (RNNs) with activation functions being rectified linear units (ReLUs). In particular, we focus on the linear nonegative properties of the input-output signals of ReLUs. To capture these linear properties within the framework of integral quadratic constraint (IQC), we introduce a copositive multiplier constructed from a copositive matrix. This enables us to capture the linear input-output properties of ReLUs in quadratic form. By using the copositive multipliers in additon to existing multipliers, we can reduce the conservatism of the IQC-based stability analysis for RNNs. We also show that the proposed IQC-based stability condition with copositive multipliers can be viewed as an extension of a recently proposed scaled small-gain stability condition based on the L2+ induced norm.</p>

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