Question: Problem 2 (25 pts) Consider the system below: 1 1 1 15 1 x2 = 0 2 3 12 S + 7 005 3

Problem 2 (25 pts) Consider the system below: 1 1 1 15 1 x2 = 0 2 3 12 S + 7 005 3 2 The solution vector of the system is given by: (5) x(t) = (t) x(0) + - (t7) Bu(r) dr (6) Homog. sol. x Particular sol. Xp x1(t) or, x(t) = x(t) + xp(t) = x2(t) x3(t) Let us assume the initial conditions as: The input is given as: X0= = [1 0.5 0.1] u(t) = et (7) (a) (10 pts) Find the analytical expression for x(t). (b) (10 pts) Find the analytical expression for xp(t). (c) (5 pts) Find the value of t to satisfy a3(t) = 1. In other words, considering the input and the system dynamics, at what time, does 3(t) reach to 1?

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