1. **State the problem:** Determine the stability of the system with characteristic polynomial $$p(z) = z^6 + 2z^5 + 3z^4 + 5z^3 + 18z^2 + 4z + 16$$ using the Jury stability test. 2. **Recall the Jury stability test:** For a polynomial $$p(z) = a_0 z^n + a_1 z^{n-1} + \cdots + a_n$$ with $a_0 = 1$ (monic), the system is stable if all roots lie inside the unit circle. The Jury test involves constructing a tabular array and checking conditions on the coefficients. 3. **Write coefficients:** $$a_0=1, a_1=2, a_2=3, a_3=5, a_4=18, a_5=4, a_6=16$$ 4. **Check first condition:** $$|a_n| < a_0$$ means $$|16| < 1$$ which is false. Since $|a_6|=16$ is not less than $a_0=1$, the system is immediately unstable. 5. **Conclusion:** Because the last coefficient's magnitude exceeds the first coefficient, the polynomial has roots outside the unit circle, so the system is unstable. **Final answer:** The system is **not stable** according to the Jury stability test.