Stabilization of some fractional delay systems of neutral type

In this note, we give new stability tests which enable one to fully characterize the H∞H∞-stability of systems with transfer function G(s)=r(s)p(s)+q(s)e-sh, where h>0h>0 and p,q,rp,q,r are real polynomials in the variable sμsμ for 0<μ<10<μ<1.As an application of this, in the case r(s)=1r(s)=1 and degp=degq=1degp=degq=1, families of H∞H∞-stabilizing controllers are given and a complete parametrization of all H∞H∞-stabilizing controllers is obtained when |lims∈C⧹R-|s|→∞p(s)/q(s)|>1.