JURY’S STABILITY TEST
Jury’s stability test is similar to the Routh–Hurwitz stability criterion used for continuous- time systems. Although Jury’s test can be applied to characteristic equations of any order, its complexity increases for high-order systems.
To describe Jury’s test, express the characteristic equation of a discrete-time system of order
The necessary and sufficient conditions for the characteristic equation (8.3) to have roots inside the unit circle are given as
• Check the three conditions given in (8.4) and stop if any of these conditions is not satisfied.
• Construct the array given in Table 8.1 and check the conditions given in (8.5). Stop if any condition is not satisfied.
Jury’s test can become complex as the order of the system increases. For systems of or- der 2 and 3 the test reduces to the following simple rules. Given the second-order system characteristic equation
