This chapter is concerned with the various techniques available for the analysis of the stability of discrete-time systems.
Suppose we have a closed-loop system transfer function
where 1 + GH(z) =0 is also known as the characteristic equation. The stability of the system depends on the location of the poles of the closed-loop transfer function, or the roots of the characteristic equation D(z) = 0. It was shown in Chapter 7 that the left-hand side of the s-plane, where a continuous system is stable, maps into the interior of the unit circle in the z-plane. Thus, we can say that a system in the z-plane will be stable if all the roots of the characteristic equation, D(z) = 0, lie inside the unit circle.
There are several methods available to check for the stability of a discrete-time system:
The various techniques described in this section will be illustrated with examples. ...