The Jury stability test

In the same way that the Routh-Hurwitz criterion offers a simple method of determining the stability of continuous systems, the Jury (1958) stability test is employed in a similar manner to assess the stability of discrete systems. 

Consider the characteristic equation of a sampled-data system 

The array for the Jury stability test is given in Table 7.4 where 

The neeessary and suffieient eonditions for the polynomial Q(z) to have no roots outside or on the unit eirele are 

In Example 7.4, the solution was found assuming that K=. Therefore, using equation (7.53), the eharaeteristie equation is 

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The seript file examp75.m simulates the Jury stability test undertaken in Example 7.5. With the eontroller gain K in Example 7.5 (Figure 7.14) set to 9.58 for marginal stability see equation (7.75), the roots of the denominator of the elosed-loop pulse transfer funetion are ealeulated, and found to lie on the unit eirele in the z-plane. 

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