# lecture8 - EE313 Linear Systems and Signals Fall 2010...

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Unformatted text preview: EE313 Linear Systems and Signals Fall 2010 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 8 - 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 8 - 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 → ∞ 8 - 4 Characteristic Modes • Distinct characteristic roots λ 1 , λ 2 , …, λ n ( 29 { } { } { } ∞ = < = = ∞ → = ∑ Re if Re if Re if lim 1 λ λ e λ e e c t y t j t t n j t j j ϖ...
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lecture8 - EE313 Linear Systems and Signals Fall 2010...

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