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Problems: Consider the following system, G11(s) G12(8) G21 (s) G22(s) S+I S+2 G(s) 1S+2 s+1 and answer the following questions 1. Find the poles and zeros for each SISO transfer function G1 (s), G12(s), G21 (s) and G22(s) 2. For each SISO transfer function, eg, Yu (s) = G11(s)U1 (s), calculate a state space realization. 3. Explain how to obtain G(s) by connecting the four SISO transfer functions from 2 and calculate a state space realization for G(s) based on that connection Note: Y(s)=G(s)U(s), U(s)=(U! (s), U2(s))*, Y(s)=(Yi(s), Vols)), Yi (s)=Yu(s) + Y12(s). 4. What is the order for MIMO state space realization of G(s)? What are the poles? 5. Is the state space realization obtained in 3 observable? If not, explain why. 6. Is the state space realization obtained in 3 controllable? If not, explain why. 7. Is the state space realization obtained in 3 minimal? If not, explain why. 8. Now use MATLAB command tf to create G(s) and use command ss to get the state space realization of G(s). Answer question 4, 5, 6, and 7 for the state space realization produced by MATLAB 9. Use MATLAB command tzero to obtain the transmission zeros for both realization in 3 and 8 10. (Bonus) What is a transmission zero? Why are answers for questions 4 to 7 different for the realization obtained in 3 and 8?

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Problems: Consider the following system, G11(s) G12(8) G21 (s) G22(s) S+I S+2 G(s) 1S+2 s+1 and...
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