Time-Delay Systems

Time-delay systems can be specified in multiple ways and conveniently converted between state-space and transfer-function representations.

A time-delay system specified as an ODE:
A system specified using state-space matrices and the SystemsModelDelay operator:
A system specified as a transfer function:
A transfer function with delays specified using SystemsModelDelay:
A discrete-time system is determined with the SamplingPeriod option:
Convert between state-space and transfer-function representations:
Obtain the discrete-time approximations of continuous-time systems and vice versa: