Absolute instability of Lur'e systems and its application to oscillation analysis of uncertain genetic networks

作者：Inoue Masaki^*; Imura Jun ichi; Kashima Kenji; Suzuki Masayasu; Aihara Kazuyuki

来源：International Journal of Robust and Nonlinear Control, 2015, 25(18): 3746-3762.

DOI：10.1002/rnc.3294

• absolute instability
• Lur'e systems
• uncertain systems
• biological systems

We derive instability criteria for Lur'e systems with sector-bounded nonlinearities and uncertain external signals. First, we define absolute instability of an equilibrium and derive an absolute instability condition for a fixed equilibrium point in terms of a linear matrix inequality, which is analogous to the well-known circle stability criterion. Then, the condition is extended to a parametric absolute instability condition, which is applicable to the instability test of a Lur'e system with an equilibrium point whose location is affected by uncertain nonlinearities and uncertain external signals. Finally, we show that the proposed analysis method is useful through the oscillation analysis of an uncertain genetic network model.

• 出版日期2015-12