Reflects polynomial roots located outside the unit circle to the inside.
POLYSTAB(a)
a |
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A series or matrix. The polynomial coefficients in descending order. |
A series, the coefficients of the reflected polynomial.
W1: {1, -2, 5}
W2: polystab(W1)
W3: zplane({1}, W1)
W4: zplane({1}, W2)
W1 represents the coefficients of the polynomial:
The roots of the polynomial are 1 + 2i and 1 – 2i, outside the unit circle. If these coefficients represent the denominator polynomial of a digital system, the system is unstable.
W2 == {1, -.4, .2}, the coefficients of the reflected polynomial. The roots of this polynomial are 0.2 + 4i, 0.2 - 4i, inside the unit circle. If the coefficients represent the denominator polynomial of a digital system, the system is stable.
W3 and W4 graphically show the pole locations with respect to the unit circle.
POLYSTAB replaces the roots of a polynomial that lie outside the unit circle with roots that are inside the unit circle. Typically, the input series represents the coefficients of the following digital system: