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Absolute instability of Lur’e systems and its application to oscillation analysis of uncertain genetic networks. (English) Zbl 1336.93141

Summary: 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.

MSC:

93D99 Stability of control systems
93C15 Control/observation systems governed by ordinary differential equations
93C10 Nonlinear systems in control theory
93C41 Control/observation systems with incomplete information
34K11 Oscillation theory of functional-differential equations
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