Help me solve this ASSIGNEMENT II a) A discrete system is described by the follo

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Help me solve this

ASSIGNEMENT II a) A discrete system is described by the following difference equation Determine the y(k 2)-1.2y(k +1) +0.5y(k) u(k 1)-0.5u(k) i. The state space representation of the system in diagonal and observable canonical forms i. The pulse transfer function for the system iii. The stability of the system [10marks] b) Determine the pulse transition matrix of the discrete system represented by: x(k 1)-0.32 -1 0.32(k)+u(i) y(k) [0 1x(k). Also obtain the state x (k) and the output y (k) when the input u (k) 1 for [10marks] [10marks] 6 12 Asumethat( x101 x2 (0) c) Obtain the describing function for the nonlinearity shown in the Figure below. -b-d -M

Explanation / Answer

Hello,
       Please find the answer to the first question attached below. If the answer has helped you please give a thumbs up rating. Thank you and have a nice day!

NOTE: I have solved the first question using Matlab:

******* Matlab Code ******

%%%%%%%%%%%%%%%%%%%%%%%%%%
%% controllability and pole placement

A = [1 0.2;0.6 0.1];                    % system parameters
B = [1;0];
C = [1 1];
D = 0;
clc;

p = [0.6 0.45];                         % desired pole positions
L = place(A,B,p)                        % feedback matrix

**** Output ****

L =

    0.0500    0.4917

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