A Lyapunov–Krasovskii functional with prescribed derivative whose construction does not require the stability of system is introduced. It leads to presentation stability/instability theorems. By evaluating at initial conditions depending on fundamental matrix we are able present necessary and sufficient expressed exclusively in terms delay Lyapunov for integral systems. Some examples illustrate...

Abstract We consider a homogeneous differential operator $${\mathcal {A}}$$ A and show an improved version of Murat’s condition for -quasiaffine functions, provided that the satisfies constant rank condition. As consequence, we obtain affinity along characteristic cone implies -quasiaffinity if admits first o...