Instability criteria for Lur´e systems toward oscillation analysis of uncertain gene networks

In this paper, we derive some instability criteria for Lur´e -type nonlinear systems. First, we define absolute instability. Then, linear matrix inequality conditions for absolute instability are derived. The obtained conditions are analogous to well-known circle-type and Popov-type stability criteria. Finally, we evaluate the usefulness through an application to instability analysis of an uncertain genetic network model.