When is the Achievable Discrete-Time Delay Margin Nonzero?

This technical note considers the delay margin problem for discrete-time finite dimensional linear time-invariant (FDLTI) single-input single-output (SISO) systems. This problem has been studied extensively in continuous time - it is well-known that, given a FDLTI plant and controller forming a strictly proper stable feedback connection, closed loop stability will be maintained for small delays; hence the achievable delay margin using FDLTI control is strictly greater than zero. In this work, we show that this is not the case for discrete-time systems; indeed, we show that a FDLTI SISO discrete-time plant has an achievable delay margin strictly greater than zero if and only if it has no negative real unstable poles.