Stability Criterion 2: Lyapunov Stability Theorem
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Stability Criterion 2: Lyapunov Stability Theorem
Transcript of Stability Criterion 2: Lyapunov Stability Theorem
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Stability Criterion 2: Lyapunov Stability Theorem
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Example
XTX
murmur
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Example I X 2 2
iz 2 2
Oe xi t xi
dVf Vix 2x I 12 2 2
2XC X 12 2 12 Xz 2 27
2 5 4 1 2 4 3Z X Xz 2 22
Thus Vey D iff x 2 0
Vex 0 for all x f to
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Example EERO
Hx
vexonyOeo
This shows x o is asymp stable
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Lyapunov stability theorem
ITTI.ES
TppT7efI fx O xTPx O
O
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Lyapunov stability theorem
etiO
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Lyapunov stability theorem
von
f
It
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Time-derivative of Lyapunov function
O
U xTPx xtPxCAxJpxtxTPcAxxTATpx xTPAXxT AT A x
Let Q CAMPAThen Vex xTQx 7
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Time-derivative of Lyapunov function
IVey co
asyrup stable
Vex so
Lyapunov stable
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Recap
OO
O