Abstract
This chapter examines different definitions and tests of the stability of linear time-invariant (LTI) digital systems based on transfer function models. 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 chapter also considers input-output stability and internal stability. Thereafter it provides several tests for stability—the Routh-Hurwitz criterion, the Jury criterion, and the Nyquist criterion and defines the gain margin and phase margin for digital systems. The most commonly used definitions of stability are based on the magnitude of the system response in the steady state. If the steady-state response is unbounded, the system is said to be unstable. Finally, the chapter discusses two stability definitions that concern the boundedness or exponential decay of the system output.
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