1. **State the problem:** Determine the stability of the system with characteristic polynomial $$p(z) = z^6 + 2z^5 + 3z^4 + 5z^3 + 18z^3 + 4z + 16$$ using the Jury stability test. 2. **Simplify the polynomial:** Combine like terms for $$z^3$$: $$p(z) = z^6 + 2z^5 + 3z^4 + (5 + 18)z^3 + 4z + 16 = z^6 + 2z^5 + 3z^4 + 23z^3 + 4z + 16$$ 3. **Jury test overview:** The Jury test checks if all roots of a polynomial lie inside the unit circle (i.e., have magnitude less than 1). The polynomial must be of degree $$n$$ with coefficients $$a_0, a_1, ..., a_n$$ where $$a_0$$ is the coefficient of $$z^n$$ and $$a_n$$ the constant term. 4. **Identify coefficients:** $$a_0 = 1, a_1 = 2, a_2 = 3, a_3 = 23, a_4 = 0, a_5 = 4, a_6 = 16$$ Note: The polynomial is missing $$z^2$$ term, so $$a_4 = 0$$. 5. **Check necessary conditions:** - $$|a_6| < a_0$$? $$|16| < 1$$? No, so the polynomial fails the first necessary condition for stability. 6. **Conclusion:** Since $$|a_n| = 16$$ is not less than $$a_0 = 1$$, the system is **not stable** according to the Jury stability criterion. **Final answer:** The system is unstable.