- #1
JTC
- 100
- 6
Hello,
I am studying control theory. And I have encountered something I have never considered or thought about.
Consider a system with y as the output differential equation and u as the input.
any(n) + ... + a1y(1) + a0y = bmu(m) + ... + b1u(1) + b0u
Here, the subscripts indicate different constants (I am considering a Linear, Time Invariant system).
The superscripts indicate the order of the derivative.
I have now read that if m > n, the system is not causal.
Could someone explain:
Without reference to discrete time steps as encountered in a numerical system.
Without reference to the poles and zeros of the Laplace transform...
And with just looking at the equation above and the order of m and n, can someone explain why
m < n is the requirement for causality?
I am studying control theory. And I have encountered something I have never considered or thought about.
Consider a system with y as the output differential equation and u as the input.
any(n) + ... + a1y(1) + a0y = bmu(m) + ... + b1u(1) + b0u
Here, the subscripts indicate different constants (I am considering a Linear, Time Invariant system).
The superscripts indicate the order of the derivative.
I have now read that if m > n, the system is not causal.
Could someone explain:
Without reference to discrete time steps as encountered in a numerical system.
Without reference to the poles and zeros of the Laplace transform...
And with just looking at the equation above and the order of m and n, can someone explain why
m < n is the requirement for causality?