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Unformatted text preview: System Properties Dr. Deepa Kundur Texas A&M University Dr. Deepa Kundur (Texas A&M University) System Properties 1 / 24 System Properties Classification of DiscreteTime Systems Why is this so important? I mathematical techniques developed to analyze systems are often contingent upon the general characteristics of the systems being considered I for a system to possess a given property, the property must hold for every possible input to the system I to disprove a property, need a single counterexample I to prove a property, need to prove for the general case Dr. Deepa Kundur (Texas A&M University) System Properties 2 / 24 System Properties Terminology: Implication If “ A ” then “ B ” Shorthand: A = ⇒ B Example 1 : it is snowing = ⇒ it is at or below freezing temperature Example 2 : α ≥ 5 . 2 = ⇒ α is positive Note : For both examples above, B 6 = ⇒ A Dr. Deepa Kundur (Texas A&M University) System Properties 3 / 24 System Properties Terminology: Equivalence If “ A ” then “ B ” Shorthand: A = ⇒ B and If “ B ” then “ A ” Shorthand: B = ⇒ A can be rewritten as “ A ” if and only if “ B ” Shorthand: A ⇐⇒ B We can also say: I A is EQUIVALENT to B I A = B = Dr. Deepa Kundur (Texas A&M University) System Properties 4 / 24 System Properties Terminology: Systems I A ctstime system processes a ctstime input signal to produce a ctstime output signal. y ( t ) = H { x ( t ) } I A dsttime system processes a dsttime input signal to produce a dsttime output signal. y [ n ] = H { x [ n ] } Note : iff = “ if and only if ” Dr. Deepa Kundur (Texas A&M University) System Properties 5 / 24 System Properties Stability I Bounded InputBounded output (BIBO) stable system : every bounded input produces a bounded output I a ctstime system is BIBO stable iff  x ( t )  ≤ M x < ∞ = ⇒  y ( t )  ≤ M y < ∞ for all t ....
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This note was uploaded on 01/01/2012 for the course ECEN 314 taught by Professor Halverson during the Spring '08 term at Texas A&M.
 Spring '08
 HALVERSON

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