Question

System transformation on function H(z) for a discrete time LTI system expressed in state variable form with zero initial condition

(a) C(zI-A)^-1B+D

(b) C(zI-A)^-1

(c) (zI-A)^-1z

(d) (zI-A)^-1

This question was addressed to me in an interview for job.

Query is from Concepts of State, State Variables and State Model in chapter State Variable Analysis and Design of Control Systems

Answer 1

The correct choice is (a) C(zI-A)^-1B+D

To elaborate: Transfer function which is ratio of Laplace output to the Laplace input when the initial conditions are zero in discrete is same as continuous but in the z-domain.