Chapter 4 - Stability of digital control systems

Abstract

Stability is a basic requirement for digital and analog control systems. Digital control is based on samples and is updated every sampling period, and there is a possibility that the system will become unstable between updates. This obviously makes stability analysis different in the digital case. We examine different definitions and tests of the stability of linear time-invariant digital systems based on transfer function models. In particular, we consider input–output stability and internal stability. We provide several tests for stability: the Routh–Hurwitz criterion, the Jury criterion, and the Nyquist criterion. We also define the gain margin and phase margin for digital systems.