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Unformatted text preview: Stability EE 313 Linear Systems and Signals Fall 2008 Prof. Adnan Kavak Dept. of Electrical and Computer Engineering The University of Texas at Austin Courtesy of Prof. Brian Evans 2 Stability • Many possible definitions • Two key issues for practical systems – System response to zero input – System response to nonzero but finite amplitude (bounded) input • For zeroinput 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 3 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 zeroinput 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 4 Internal Stability • Three cases for zeroinput response – A system is stable if and only if all characteristic modes → 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 → ∞ 5 Characteristic Modes • Distinct characteristic roots λ 1 , λ 2 , …, λ n ( 29...
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This note was uploaded on 02/10/2009 for the course EE 313 taught by Professor Cardwell during the Spring '07 term at University of Texas.
 Spring '07
 Cardwell

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