Notes-3A

# Notes-3A - 3. Stability and Stabilization 3.1 Concept of...

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3. Stability and Stabilization 3.1 Concept of Stability Peak magnitude Stability of a polynomial : all roots have negative real parts. BIBO Stability : output is bounded for each bounded input . BIBO Stability : G(s) is proper and all poles have negative real parts.

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3.2 Routh Criterion
Routh Criterion

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Routh Criterion
Routh Criterion

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Routh Criterion
Routh Criterion

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Routh Criterion
Routh Criterion

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3.3 Routh Hurwitz Criterion Hurwitz matrix
Routh Hurwitz Criterion

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3.4 Robust Stability Kharitonov Theorem is stable if and only if the following four are stable are all stable.
3.5 Stability of Closed Loop Systems All transfer functions must be stable. Stable: if the characteristic polynomial is stable. 1 () 1 () () 1 : ( ) , ( ) , stable, 1( ) 1 ( ) 1 ( ) ( ) 2 ()() ( 1 ) ( 1 ) ( 1 ) Example ( 2) is unstable. bs s qs PsCs Ps Cs sa s s p s P s C s s asps bsqs s s s s s == = −+ + + += + + = +

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More Stability Tests The following are equivalent: 1. The closed-loop is stable () 2. and are stable 1( ) ( ) ) ( ) 3. Suppose ( ) is stable. Then is stable.
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## This note was uploaded on 02/03/2012 for the course EE 3530 taught by Professor Chen during the Fall '07 term at LSU.

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Notes-3A - 3. Stability and Stabilization 3.1 Concept of...

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