Determine stability by using the state space solution

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Reference no: EM13248315

Convert the following differential equation 5 (t) +4 (t) +3x.(t) + 2x(t) + 7u(t) - 5u.(t) + 2 (t) = 0 to state space form. Is this system marginally stable, asymptotically stable, or unstable when u(t) = 0? Determine stability by using the state space solution. How does it compare to the roots of the characteristic equation? For the ODE in problem 2, show that if y(t) = x(t) that Y(s)/U(s) = G(s) = C(sI3 - A)-1 B where G(s) is the transfer function found by directly converting the ODE in problem 2 to the Laplace domain assuming that x(0) = x.(0) = x(0) = 0 and A, B, C, are the matrices found in the last problem to represent the system in state space form.

Reference no: EM13248315

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