# Question 4.4: OBTAINING A STATE-SPACE MODEL FROM AN IMPULSE-RESPONSE MODEL...

OBTAINING A STATE-SPACE MODEL FROM AN IMPULSE-RESPONSE MODEL.

Find an equivalent state-space representation of the following impulse-response model:

$y(t) = \frac{K}{\tau} \int_{0}^{t}{e^{- (t – \sigma)/ \tau} u(\sigma) d \sigma}$        (4.75)

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Question: 4.5

## IMPULSE-RESPONSE FORM OF A FIRST-ORDER TRANSFORM-DOMAIN TRANSFER FUNCTION. Find the equivalent impulse-response representation of the following transformdomain transfer function model first given in Example 4.1: y(s) = g(s) u(s) (4.60a) where g(s) = K/τs + 1 (4.60b) ...

In this case, by Laplace inversion of g(s) we obta...
Question: 4.6

## OBTAINING A TRANSFER-DOMAIN FUNCTION MODEL FROM AN IMPULSE-RESPONSE MODEL. Find the equivalent transform-domain transfer function representation of the following impulse-response model: y(t) = Kt/τ² ∫0^t e^-(t – σ)/τ u(σ) dσ (4.77) ...

Observe that the impulse-response function in this...
Question: 4.3

## REALIZATION OF A FIRST-ORDER-PLUS-TIME-DELAY TRANSFORM-DOMAIN TRANSFER FUNCTION. Given the following transfer function model: y(s) = g(s) u(s) (4.69a) with g(s) = Ke^-αs/τs + 1 (4.69b) find an equivalent state-space representation. ...

Again, introducing Eq. (4.69b) into Eq. (4.69a), t...
Question: 4.2