Nonsmooth Lurie Dynamical Systems

Abstract

This chapter is dedicated to the study of Lur’e systems involving maximal monotone and nonmonotone set-valued nonlinearities. The first case is studied with a nonzero feedthrough (or feedforward) matrix D under the so-called passivity condition. In the second case, the matrix D=0 and the problem are formulated into a first-order differential inclusion form where the set-valued right-hand side is upper semicontinuous with nonempty, convex, compact values to obtain the existence of a solution. Then, local hypomonotonicity is assumed to ensure the uniqueness result. A stability analysis and LaSalle’s invariance principle are developed. Finally, some illustrative examples in power electronics are presented.