INPUT‐OUTPUT STABILITYINPUT OUTPUT STABILITY

INPUT‐OUTPUT STABILITYINPUT OUTPUT STABILITY

• Stability properties concerned with the input‐Stability properties concerned with the inputoutput behavior (zero‐state response) of the linear state equation will be addressedlinear state equation will be addressed

• Input output behavior is specified by 

Bound of a signal over timeBound of a signal over time

• The bound on a signal is defined asThe bound on a signal is defined as

• If no such bound exists then

Uniform bounded‐inputb d d bilibounded‐output stability

(Definition)( )

Uniform bounded‐inputbounded‐output stability

(Test)(Test)

Uniform bounded‐inputb d d bilibounded‐output stability

(Test)( )

BIBO stability test (LTI)BIBO stability test (LTI)

BIBO stability test (LTI)BIBO stability test (LTI)

Example LTIExample LTI

• Given systemGiven system

• Diagonalized system

Example contd.Example contd.

• Transfer functionTransfer function

• Signal flow

2

Example contd.Example contd.

• Signal flow graph of diagonalized systemSignal flow graph of diagonalized system