Consider the system m 0 0 2 ] 0 - 4 0 1 - 6 x(r), Suppose that we are given three

Chapter 0, Problem CP11.7

(choose chapter or problem)

Consider the system m 0 0 2 ] 0 - 4 0 1 - 6 x(r), Suppose that we are given three observations y(t,), i - 1,2,3, as follows: y(t{) = 1 at ?j = 0 y(t2) = -0.0256 at t2 = 2 y(t3) = -0.2522 at /3 = 4. (a) Using the three observations, develop a method to determine the initial value of the state vector x(r0) for the system in Equation CPU.l that will reproduce the three observations when simulated using the Isim function. (b) With the observations given, compute x(r0) and discuss the condition under which this problem can be solved in general, (c) Verify the result by simulating the system response to the computed initial condition. (Hint: Recall that x(f) Equation CP11.1.)