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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 Systems output due to nonzero initial conditions should approach 0 as t Systems 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 Systems output due to nonzero initial conditions should approach 0 as t Systems 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 1 , 2 , , n ( 29...
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 Spring '07
 Cardwell

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