EE 351 – Linear Systems II Homework #5 1. Write the complete set of state variable equations in matrix form for the discrete time system shown below. Answer: A =−6 −51 −3"#$%&' B =01"#$%&' C = 3 0[ ] D = −4[ ] 2. Write the complete set of state variable equations in matrix form for the discrete time system shown below. Answer: A =0 1 0−15−1300 0 0"#$$$$%&'''' B =012"#$$$%&''' C = −1 0 1[ ] D = 1[ ] unitdelayunitdelay34xkyk-+563---++unitdelayunitdelay1/3xkyk-+1/52unitdelay+-+-3. Write the complete set of state variable equations in matrix form for the discrete time system shown below. Answer: A =3 00 −4"#$%&' B =11"#$%&' C =1 00 1"#$%&' D =0−5"#$%&' 4. Write the complete set of state variable equations in matrix form for the discrete time system shown below. Answer: A =2 10 −4"#$%&' B =−1 00 1"#$%&' C = −1 3[ ] D = −1 0[ ] unitdelay3xkyk(2)++unitdelay4-+5+-yk(1)unitdelayunitdelay42xk(2)yk-+3+xk(1)-+--+5. Write the complete set of state variable equations in matrix form for the discrete time system shown below. Answer: A =0 0 00 −1 00 1 −5"#$$$%&''' B =1 01 00 1"#$$$%&''' C =2 −1 30 1 −1"#$%&' D =0 10 −3"#$%&' 6. Write the complete set of state variable equations in matrix form for the discrete time system shown below. Answer: unitdelay52xk(2)-+3xk(1)unitdelayunitdelay2+-+-++-++--yk(1)yk(2)unitdelay1/3xk+unitdelay1/2++++yk(1)yk(2)A =1/2 01/2 1/3B =11C =1 00 1D =00Read and perform the examples in MATLAB Tutorial #5 before attempting problem 7 below. 7. For the discrete time system given in problem 1: a. Create a simulink model of the block diagram using unit delays, gain blocks and summers. Use the simin and simout blocks for the input and output. Apply a unit step sequence, uk, as the input for 0 ≤ k ≤ 10. Run the simulation and list the values of the output in the MATLAB command window. Turn in a copy of your simulink diagram and the command window listing. b. Create a second simulink model of this system but this time use the Discrete State Space block to model the system. Use the A, B, C, D matrices found in problem 1. Run the simulation for the same input as part a and list the values of the output in the MATLAB command window. How does this output compare to the results of part a? Turn in a copy of the simulink diagram and the command window