4.8 An LTI system is described by the following differential equations: Let x1(0) 1, x2(0) ...

4.8 An LTI system is described by the following differential equations:

Let x1(0) ¼ 1, x2(0) ¼ 1, and u(t) ¼ et; derive expressions for x1(t) and x2(t).

(a) Find a nonsingular transformation matrix T such that the change in variables z ¼ Tx will lead to a decoupled system of differential equations.

(b) Solve the decoupled system for the new variables z1(t) and z2(t), and demonstrate that your results are consistent with the results obtained for x1(t) and x2(t).

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X2(1) = -2 x(t) x2(1) + +8 u(t)