Notes-3B

# Notes-3B - 9/21/2009 3. Stability and Stabilization 3.1...

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9/21/2009 1 3. Stability and Stabilization 3.1 Concept of Stability Peak magnitude BIBO Stability : output is bounded for each bounded input . BIBO Stability : G(s) is proper and all poles have negative real parts. Stability of a polynomial : all roots have negative real parts. 3.2 Routh Criterion

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9/21/2009 2 Routh Criterion Routh Criterion
9/21/2009 3 Routh Criterion Routh Criterion

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9/21/2009 4 Routh Criterion Routh Criterion
9/21/2009 5 Routh Criterion 3.3 Routh Hurwitz Criterion Hurwitz matrix

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9/21/2009 6 Routh Hurwitz Criterion 3.4 Robust Stability Kharitonov Theorem is stable if and only if the following four are stable are all stable.
9/21/2009 7 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( ) ) ) ( ) 2 ()() ( 1 ) ( 1 ) ( 1 ) Example (2 ) i s u n s t a b l e . bs s qs PsCs Ps Cs sa s sp sP s C s s asps bsqs s s s s s == = −+ + + += + + = + More Stability Tests The following are equivalent: 1. The closed-loop is stable 2. and are stable ) ( ) ) ( ) 3. Suppose ( ) is stable. Then

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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-3B - 9/21/2009 3. Stability and Stabilization 3.1...

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