Generating State Variable Description

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To convert the given second-order differential equation into state-space form, define the state vector as x = [y, \dot{y}]^T. The matrices can be determined as A(t) = [[0, 1], [-3, -2]], B(t) = [0; 1], C(t) = [1, 0], and D(t) = 0. The state-space equations will be \dot{x} = A(t)x + B(t)\dot{u} and y = C(t)x + D(t)\dot{u}. This formulation allows for analysis and control design of the system described.
hadron23
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Hello,

I came across a problem in some literature and was curious about how to solve it,

Given a system described by,

\ddot{y} + 2\dot{y} - 3y = \dot{u} - u

Convert the above into state-space form with input \dot{u} and output y.

Define the state vector and determine the matrices A(t),B(t),C(t),D(t) such that,

\dot{x} = A(t)x + B(t)\dot{u}
y = C(t)x + D(t)\dot{u}

Any ideas?
 
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Can anybody tell me what will be the state space equation for the circuit in the below link. I will be very happy to know this.http://i783.photobucket.com/albums/yy113/sandhi_prashant/Statespaceequation.jpg

with regards,
Sandhi
 
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