The system described by the equations (a) Use (2-89) to solve for x(k), k 0. (b) Find

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The system described by the equationsx(*+1) = 10 0 0.5 (1) + [2]) 1y(k)= [1 2]x(k) is excited by the initial conditions x(0)=[-1 2 with u(k) = 0 for all k.


(a) Use (2-89) to solve for x(k), k ≥0.

(b) Find the output y(z) .

(c) Show that Φ(k) in (a) satisfies the property Φ(0) = I.

(d) Show that the solution in part (a) satisfies the given initial conditions.

(e) Use an iterative solution of the state equations to show that the values y(k) , for k = 0, 1, 2, and 3, in part (b) are correct.

Equation 2-89k1 x(k) = (k)x(0) + ( - 1 - j)Bu(j) j=0

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Digital Control System Analysis And Design

ISBN: 9780132938310

4th Edition

Authors: Charles Phillips, H. Nagle, Aranya Chakrabortty

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