面向网络化动力学系统的精确鲁棒不稳定性分析及生物学应用
Exact Robust Instability Analysis for Networked Dynamical Systems with Biological Application
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中文总结 AI 辅助
本文针对名义不稳定的不确定网络化动力学系统，确定三类可简化分析的网络结构，推导鲁棒不稳定性半径的充分条件，并将结果应用于遗传调控网络的振荡行为分析。
中文摘要 AI 辅助
本文研究名义上不稳定的不确定网络化动力学系统中的鲁棒不稳定性，其中所有名义智能体共享一个相同的单输入单输出（SISO）线性时不变（LTI）系统，且每个智能体均受独立扰动影响。该研究背景源于非线性动力学中维持周期振荡的问题，而对此类问题的精确分析通常难以处理。我们确定了三类网络结构，包括循环网络及特定秩亏网络，这些网络的鲁棒不稳定性问题可简化为对单个代表性SISO系统的分析。我们推导了能精确表征此类网络鲁棒不稳定性半径的充分条件。最后，我们通过分析遗传调控网络中的振荡行为，验证了所提结果的实际应用价值。
英文摘要
This paper investigates robust instability in nominally unstable uncertain networked dynamical systems, where all nominal agents share an identical single-input-single-output (SISO) linear time-invariant (LTI) system and each agent is subject to independent perturbations. This setting is motivated by the problem of sustaining periodic oscillations in nonlinear dynamics, for which exact analysis is generally intractable. We identify three classes of network structures including cyclic and certain rank-deficient networks for which the robust instability problem can be reduced to the analysis of a single representative SISO system. We derive sufficient conditions that exactly characterize the robust instability radius for these network classes. Finally, we demonstrate the practical utility of the proposed results by analyzing oscillatory behavior in a genetic regulatory network.
