Is the Zero State Response Unaffected by Initial Conditions?

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Discussion Overview

The discussion revolves around the concept of zero state response (ZSR) in systems theory, specifically whether it is influenced by initial conditions. Participants explore the definitions and implications of ZSR in the context of state space problems.

Discussion Character

  • Conceptual clarification, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant asserts that the zero state response is never affected by initial conditions.
  • Another participant clarifies that ZSR is defined as the response of the system when initial conditions are zero, suggesting that initial conditions do influence the response in certain contexts.
  • A participant explains that in a state space problem, the zero state response is derived by excluding terms related to initial conditions, leading to the conclusion that ZSR yields the same result regardless of initial conditions.
  • There is a challenge regarding the understanding of ZSR, emphasizing that it is calculated under the assumption that all initial conditions are zero.
  • A later reply indicates a realization about the definition of ZSR and its dependence on initial conditions.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between zero state response and initial conditions. While some clarify the definition and implications of ZSR, there is no consensus on the initial claim regarding its independence from initial conditions.

Contextual Notes

The discussion highlights potential misunderstandings about the definition of zero state response and its calculation, particularly in relation to initial conditions and system order.

LM741
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do you guys aggree with this:

The zero state response is never affected by initial conditions.

thanks
 
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It depends on what you mean by affected. Zero state response is the response of the system when the initial conditions are zero. So the initial value of the response is 0 and in a system of order equal or greater than two, the initial slope of the response will also be 0. So in this sense the initial state influences the response.
But if there is no excitation, the system will remain in the zero state and the response will not be influenced.
 
what i mean by affected is: you will always get the same answer for sero state response regardless of what the initial condition are. i.e. there is no correlation.
I came to this conclusion whilst doing a state space problem that requires the zero state response. In the textbook, they first derive a solution for X(z)
, working in discrete. This X(z) is actually made up of two terms, where the one term includes the inital conditions. To solve for the ZSR they exclude the term with the initail condititions and work from there...

thanks
 
LM741 said:
what i mean by affected is: you will always get the same answer for sero state response regardless of what the initial condition are. i.e. there is no correlation.
...
thanks
Do you really understand what zero state response means? By definition, ZSR is the response of the system when all initial conditions are zero. How can you calculate ZSR with varying initial conditions?
 
yup i just realized that.
thanks
 

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