961ls02System2

# 961ls02System2 - Fall 2007 Linear Systems Chapter 02...

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Fall 2007 線性系統 Linear Systems Chapter 02 Mathematical Descriptions of Systems 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) Outline ± Introduction ± Linear Systems (2.2) ± Linear Time-Invariant Systems (2.3) ± Linearization (2.4) ± Examples (2.5) ± Discrete-Time Systems (2.6)

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Introduction: What is a system? – 1 (2.1) NTUEE-LS2-System-4 Feng-Li Lian © 2007 Introduction: What is a system? – 2 ¨ A “mapping” from input signal(s) to output signal(s) Excitation Input Cause Response Output Effect System
NTUEE-LS2-System-5 Feng-Li Lian © 2007 System Characteristics – 1 • Continuous-Time systems: • Single-Input-Single-Output ( SISO ) systems: • Discrete-Time systems: • Multi-Input-Multi-Output ( MIMO ) systems: NTUEE-LS2-System-6 Feng-Li Lian © 2007 System Characteristics – 2 • Memoryless systems: ¾ y ( t 0 ) depends only on u ( t 0 ) •Dynam ic systems: ¾ y ( t 0 ) depends on u ( t ) • Causal systems: ¾ y ( t 0 ) depends only on u ( t ) , t t 0 •Non-causa l (anticipatory) systems: ¾ y ( t 0 ) depends on u ( t ) , t t 0

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NTUEE-LS2-System-7 Feng-Li Lian © 2007 System Characteristics – 3 • Lumped systems: ¾ Finite number of state variables • Distributed systems: ¾ Infinite number of state variables NTUEE-LS2-System-8 Feng-Li Lian © 2007 Concept of System States – 1 (2.1.1) ± Parameters: ± Variables: ± State Variables: ± Inputs: ± Outputs:
NTUEE-LS2-System-9 Feng-Li Lian © 2007 Concept of System States – 2 x(t) u(t) y(t) NTUEE-LS2-System-10 Feng-Li Lian © 2007 Concept of System States The output is partly excited by the initial state at t 0 and partly by the input applied at and after t 0 . Therefore, there is no need to know the input applied before t 0 all the way back to – In general, state variables may or may not have physical meanings.

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Linear Systems – 1 (2.2) Linear systems satisfy the superposition property, that is, Imply (1) additivity And (2) homogeneity NTUEE-LS2-System-12 Feng-Li Lian © 2007 Linear Systems – 2 • Zero-input response:
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## This note was uploaded on 07/21/2009 for the course EE 901-43400 taught by Professor Feng-lilian during the Fall '08 term at National Taiwan University.

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961ls02System2 - Fall 2007 Linear Systems Chapter 02...

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