Identifying Impulse Response Function from State Equations

[khedira]

Hi,

given the state equations of a system,

x(dot) = Ax + Bu
y = Cx

is the impulse response function of this system C(e^(At))B? If not, how can i identify the impulse response from a given state equations? Please advise. Thank you.

 

[HallsofIvy]

Hi,

given the state equations of a system,

x(dot) = Ax + Bu
y = Cx

is the impulse response function of this system C(e^(At))B? If not, how can i identify the impulse response from a given state equations? Please advise. Thank you.

What you have written makes no sense. I recognize that "x(dot)" is the derivative of x with respect to t but do you mean to have a "dot" next to the y in the next line? And what is "u"? Was that supposed to be y?

That is, is the problem really
$$\frac{dx}{dt}= Ax+ By$$
$$\frac{dy}{dt}= Cx$$
?

 

[khedira]

What you have written makes no sense. I recognize that "x(dot)" is the derivative of x with respect to t but do you mean to have a "dot" next to the y in the next line? And what is "u"? Was that supposed to be y?

That is, is the problem really
$$\frac{dx}{dt}= Ax+ By$$
$$\frac{dy}{dt}= Cx$$
?

Oh so sorry, i thought what i have given is the general representation of a state space equation, where x is the state variable, u is the input and y is the output. and yes, "x(dot)" is the derivative of x with respect to t but y is just y.