lecture6

# lecture6 - EE313 Linear Systems and Signals Spring 2009...

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EE313 Linear Systems and Signals Spring 2009 Initial conversion of content to PowerPoint by Dr. Wade C. Schwartzkopf Prof. Brian L. Evans Dept. of Electrical and Computer Engineering The University of Texas at Austin Stability

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6 - 2 Stability Many possible definitions Two key issues for practical systems System response to zero input: internal stability System response to non- zero but finite amplitude (bounded) input: bounded input bounded output (BIBO) stability For zero-input response If a system remains in a particular state (or condition) indefinitely, then state is an equilibrium state of system System’s output due to nonzero initial conditions should approach 0 as t →∞ System’s output generated by initial conditions is made up of characteristic modes
6 - 3 Stability Three cases for zero-input response A system is stable if and only if all characteristic modes go to 0 as t A system is unstable if and only if at least one of the characteristic modes grows without bound as t A system is marginally stable if and only if the zero-input response remains bounded (e.g. oscillates between lower and upper bounds) as t

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Characteristic Modes Distinct characteristic roots λ 1 , λ 2 , …, λ n ( 29 { } { } { } = < = = = 0 Re if 0 Re if 0 Re if 0 lim 1 0 λ λ e λ e e c t y t j t t n j t j j ϖ λ Where λ = σ + j ϖ plane (RHP)
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## This note was uploaded on 01/22/2012 for the course EE 313 taught by Professor Cardwell during the Spring '07 term at University of Texas.

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lecture6 - EE313 Linear Systems and Signals Spring 2009...

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