3' Instantaneous and Dynamic Systems

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• 3. Instantaneous and Dynamic Systems
• A system is said to be instantaneous (or,
  memoryless), if the present value of its output
  depends only on the present value of its input

• Example 1 R is a resistor
• This system is memoryless

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• Example 2 C is a capacitor
• This system is with memory, because
• A linear time-variant memoryless system
• A linear time-invariant memoryless system

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• 4. Other Classifications
• Causal and Non-causal Systems
• Lumped and distributed parameter systems
• Discrete-time systems

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• Chapter 2
• Time-Domain Analysis of LTIC Systems
• LTIC means Linear, Time-Invariant,
  Continuous-Time
• 2-1 Response of a Linear System
• Consider SISO (single-input, single-output)
  cases
• A systems output for depends on two
  causes
• (1) Initial conditions at
• (2) Input for
• i.e. There are two parts in the output (a)
  zero-input response (b) zero-state response

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• Example 1 RC circuit (Fig. 1.26)

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• Zero-Input (Z-I) response
• Result of internal system conditions
• Zero-State (Z-S) response
• Result of external input
• The Z-I and Z-S responses are independent each
  other
• Example 2 (RLC circuit, p. 80 and p. 111 of
  textbook)

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• Example

• The characteristic polynomial, equation, roots,
  and modes

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• Caveat !
• The output can also be expressed in another way
• Total output natural response forced response
• This concept is different than Z-I and Z-S
  concepts
• You should have known this in the Circuit
  course(s)
• Read Example 2.2 in p. 111 to refresh your
  memory and enhance your understanding