Abstract
Parametric absolute stability is the concept of stability which deals with feasibility and stability of equilibrium states of Lur'e systems with parametric linear parts and sectorial bounded nonlinearities. A Popov-type sufficient condition for parametric absolute stability has been obtained for single-variable Lur'e systems. For multivariable Lur'e systems, a condition in the state space, which is described by linear matrix inequalities (LMIs), has been derived. For polytopic Lur'e systems, the LMIs are easily solved by a computational tool. However, if the linear part is nonlinear with respect to parameters, there exists no useful tool solving the LMIs. In this paper, the Popov-type condition of parametric absolute stability is extended to multivariable Lur'e systems. An example is presented, in which the condition is tested by applying the polygon interval arithmetic (PIA).
