Stabilization of some fractional delay systems of neutral type

Abstract

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