arXiv subjects

Tsuyoshi Yuno

Publications and source records attributed to Tsuyoshi Yuno.

3 recordsLinked to original sources

arXiv2025

LMI hierarchies for stability analysis of ReLU feedback systems

We consider the stability analysis of feedback systems with rectified linear unit (ReLU) activations, and model this problem with polynomial optimization. Stability can be certified by means of copositive multipliers in the framework of integral quadratic constraints. Based on a duality argument, we show how to certify instability by considering a complete hierarchy of linear matrix inequalities. This hierarchy is obtained by leveraging the specific equality constraints arising from the ReLU encoding. We illustrate the effectiveness of the proposed approach through several numerical examples.

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arXiv2025

Detecting Destabilizing Nonlinearities in Absolute Stability Analysis of Discrete-Time Feedback Systems

This paper is concerned with the absolute stability analysis of discrete-time feedback systems with slope-restricted nonlinearities. By employing static O'Shea-Zames-Falb multipliers in the framework of integral quadratic constraints, we can obtain a certificate for the absolute stability in the form of a linear matrix inequality (LMI). However, since this LMI certificate is only a sufficient condition, we cannot draw any definite conclusion if the LMI turns out to be infeasible. To address this issue, we focus on the dual LMI that is feasible if and only if the original (primal) LMI is infeasible. As the main result, if the dual solution satisfies a certain rank condition, we prove that we can detect a destabilizing nonlinearity within the assumed class of slope-restricted nonlinearities as well as a non-zero equilibrium point of the resulting feedback system, thereby we can conclude that the system of interest is never absolutely stable. The effectiveness of the technical results is demonstrated through numerical examples.

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arXiv2024

On Dual of LMIs for Absolute Stability Analysis of Nonlinear Feedback Systems with Static O'Shea-Zames-Falb Multipliers

This study investigates the absolute stability criteria based on the framework of integral quadratic constraint (IQC) for feedback systems with slope-restricted nonlinearities. In existing works, well-known absolute stability certificates expressed in the IQC-based linear matrix inequalities (LMIs) were derived, in which the input-to-output characteristics of the slope-restricted nonlinearities were captured through static O'Shea-Zames-Falb multipliers. However, since these certificates are only sufficient conditions, they provide no clue about the absolute stability in the case where the LMIs are infeasible. In this paper, by taking advantage of the duality theory of LMIs, we derive a condition for systems to be not absolutely stable when the above-mentioned LMIs are infeasible. In particular, we can identify a destabilizing nonlinearity within the assumed class of slope-restricted nonlinearities as well as a non-zero equilibrium point of the resulting closed-loop system, by which the system is proved to be not absolutely stable. We demonstrate the soundness of our results by numerical examples.

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