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961ls05Stability2 - Fall 2007 Linear Systems Chapter 05...

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Fall 2007 線性系統 Linear Systems Chapter 05 Stability Feng-Li Lian NTU-EE Sep07 – Jan08 Materials used in these lecture notes are adopted from “Linear System Theory & Design,” 3rd. Ed., by C.-T. Chen (1999) NTUEE-LS5-Stability-2 Feng-Li Lian © 2007 Outline Introduction Input-Output Stability (5.2) Internal Stability (5.3) Lyapunov Theorem (5.4)
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NTUEE-LS5-Stability-3 Feng-Li Lian © 2007 Basic Concept (5.1) Stable Systems ¨ Bounded Input and Bounded Output ( BIBO ) Stability Unstable Systems ¨ Small Input generates Unbounded Output Response of Linear Systems ¨ Zero-State Response + Zero-Input Response ¨ BIBO Stability + Marginal/Asymptotic Stability ¨ Input-Output Stability + Internal Stability System Definition: NTUEE-LS5-Stability-4 Feng-Li Lian © 2007 Input-Output Stability (5.2) Bounded Signal s(t): ¨ a constant bound b < , s.t. | s ( t ) | ≤ b , t 0 System Bounded-Input-Bounded-Output ( BIBO ) Stable Systems: ¨ EVERY bounded input excites a bounded output ¨ Bounded outputs in response to ALL bounded inputs ¨ (zero-state response only) An SISO causal LTI systems: Definition:
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