Absolute stability of Lur'e systems with time-varying delay

The problem of the absolute the stability of Lur'e systems with time-varying delay is addressed. Full consideration is given to two cases of time-varying delays – one being continuous-uniformly bounded and the other being differentiable-uniformly bounded with the derivative of the delay bounded by a constant. Some delay-dependent absolute-stability criteria are derived and formulated in the form of linear matrix inequalities. The relationship between the absolute stability criteria for the two cases of time-varying delays is built. A numerical example shows the effectiveness of the obtained results.