Parametric Absolute Stability of Multivariable Lur'e Systems

Linear Matrix Inequalities and an Application to Polytopic Systems

Abstract

Parametric absolute stability is considered for multivariable Lur'e systems consisting of linear parts with uncertain parameters and sectorial bounded nonlinearities. The change of the equilibrium state is dealt with, which is caused by the variation of parameters and reference inputs. Linear matrix inequalities (LMIs) are derived, which constitute a sufficient condition for parametric absolute stability. They are to be satisfied for each value of the parameter vector and a specified class of nonlinearities. One of them ensures the existence of an equilibrium and is used to compute a region where it exists. Others ensure global asymptotic stability of any equilibrium in the region. For Lur'e systems with polytopic linear parts, non-parametric LMIs are presented. They are more conservative than the parametric ones, but can easily be checked via an existing tool for computation.