Old spec 3.5 example, fourth order Hurwitz determinant (ENGR5001)

Old spec 3.5 example, fourth order Hurwitz determinantTutorialOld spec ENGR2022:210 min

ENGR202 (old spec) Control 3.5 Hurwitz Stability Criterion, fourth order example (slides 4-6)

A system has the characteristic equation $2.5s^4 + 1.3s^3 + 0.02s^2 - s + 5 = 0$ Write down the 4th order Hurwitz determinant and use its principal minors to determine the stability.

Formulas you may need

Hurwitz determinant for $a_0s^n + a_1s^{n-1} + \dots + a_n = 0$ : rows $(a_1, a_3, a_5, \dots)$ , $(a_0, a_2, a_4, \dots)$ , then the same pair shifted one column right, and so on; stable if all principal minors $\Delta_1, \dots, \Delta_n > 0$ (learn this)
Necessary condition: all coefficients present and of the same sign (learn this)

Delta_1 =

Delta_2 =

Delta_3 =