Bistritz stability criterion

In signal processing and control theory, the Bistritz criterion is a simple method to determine whether a discrete, linear, time-invariant (LTI) system is stable proposed by Yuval Bistritz. Stability of a discrete LTI system requires that its characteristic polynomial D n ( z ) = d 0 + d 1 z + d 2 z 2 + ⋯ + d n − 1 z n − 1 + d n z n {\displaystyle D_{n}(z)=d_{0}+d_{1}z+d_{2}z^{2}+\cdots +d_{n-1}z^{n-1}+d_{n}z^{n}} (obtained from its difference equation, its dynamic matrix, or appearing as the denominator of its transfer function) is a stable polynomial, where d n > 0 {\displaystyle d_{n}>0} and D n ( z ) {\displaystyle D_{n}(z)} is said to be stable if all its roots (zeros) are inside the unit circle, viz.

Source: Wikipedia — Bistritz stability criterion (CC BY-SA 4.0)

Bistritz stability criterion

In signal processing and control theory, the Bistritz criterion is a simple method to determine whether a discrete, linear, time-invariant (LTI) system is stable proposed by Yuval Bistritz. Stability of a discrete LTI system requires that its characteristic polynomial D n ( z ) = d 0 + d 1 z + d 2 z 2 + ⋯ + d n − 1 z n − 1 + d n z n {\displaystyle D_{n}(z)=d_{0}+d_{1}z+d_{2}z^{2}+\cdots +d_{n-1}z^{n-1}+d_{n}z^{n}} (obtained from its difference equation, its dynamic matrix, or appearing as the denominator of its transfer function) is a stable polynomial, where d n > 0 {\displaystyle d_{n}>0} and D n ( z ) {\displaystyle D_{n}(z)} is said to be stable if all its roots (zeros) are inside the unit circle, viz.

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Source: Wikipedia "Bistritz stability criterion" · CC BY-SA 4.0

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