On the strong stabilization of delay systems

The authors address the problem of stabilizing delay systems with stable linear time-invariant controllers, i.e. the problem of strong stabilization. In particular, they consider a SISP pure-delay system of the form P(s)=e^{- hs}P₀(s). It is shown that P (s) is strongly stabilizable if and only if the poles and zeros of P₀(s) satisfy the parity interlacing property, i.e. between any two real right-half-plane poles there is an even number of real right-half-plane zeros. The results can be extended to arbitrary MIMO plants using the algebra of F.M. Callier and C.A. Desoer (1987)