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Can the output of a BIBO stable positive feedback system grow more than its input?

thread236-492803

Can the output of a BIBO stable positive feedback system grow more than its input?

Can the output of a BIBO stable positive feedback system grow more than its input?

(OP)
I am using an IIR filter which is a second order system which has zeros and poles such that the system is asymptotically stable.
The passband gain of the filter is unity.
The input range to the filter is [4,-4].
Will the output ever exceed the limits of the input due to the positive feedback in the discrete system even though the system is completely stable?

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