ABSOLUTE STABILITY OF GENERAL LURIE DISCRETE NONLINEAR CONTROL SYSTEMS

1 IntroductionUp to now, there are many results about abso1ute stability for Lurie discrete controlsystems{'--'l. Some sufficient conditions and necessary and sufficient conditions of absolutestability are obtained. But there are a few resuIts about gener…     

STABILIZATION OF NONLINEAR SYSTEMS WITH HOMOGENEOUS STABILITY

1.IntroductionTheconceptsofrelativedegreeandzerodynamicshavebeenproposedbyByrnes,Isidoriandotherstotreatlocalfeedbackstabilizationproblemofnonlinearcolltrolsystems.Oneofthekeypointsforthismethodistousecelltermanifoldtheory.[1]wasoneoftheearliestworksusingcentermanifoldtechniqueinthisarea.Firstofall,wewilldescribethecentermanifoldmethodthroughanexampletoshowhowthecentermanifoldmethodcanbeusedtosolvethestabilizationproblem.Forconvenience,wecitesomebasicresultsfrom[2].Theorem1.1Considerasystemw…     

ASYMPTOTIC STABILITY OF VISCOUS SHOCK PROFILE FOR NON-CONVEX SYSTEM OF ONE-DIMENSIONAL VISCOELASTIC MATERIALS WITH BOUNDARY EFFECT

1 IntroductionWe consider the system of one-dimensiona1 viscoelastic materials with non--convekity of thefOrm.with the illitial-boundary conditionshere v is the strain, u is the ve1ocity p > 0 is the viscous constallt, v and u are givenconstants, a is the pressure to be a known smooth fUnction of v satisfying the fOllOwing signconditions:a'(v) > 0 fOr all v u-nder consideration, (1.4)a"(v) 2 0 fOr v 2 0 under consideration, (l.5)so that rr(v) has a point of inflection at v = 0. We see that…