3. Consider the continuous-time system whose model is represented in state space by the following set of matrices: A=10 11 A L -0.5 -0.21 B = 10.21 C = [0.5 1] D = 0 (a) What is the continuous time transfer function corresponding to this system? (b) Obtain the difference equations that approximate this system for a sampling time Ts seconds using the (1) Tustin Transformation and then (2) Euler backward difference formula. (c) What are the poles of these discrete time systems? Is the discrete-time system stable for both approximations? (d) Assume that Ts= 0.02. Draw the bode plots (using MATLAB) for the original continuous time system and the two approximated systems. Comment on their differences and similarities. [25] 3. Consider the continuous-time system whose model is represented in state space by the following set of matrices: A=10 11 A L -0.5 -0.21 B = 10.21 C = [0.5 1] D = 0 (a) What is the continuous time transfer function corresponding to this system? (b) Obtain the difference equations that approximate this system for a sampling time Ts seconds using the (1) Tustin Transformation and then (2) Euler backward difference formula. (c) What are the poles of these discrete time systems? Is the discrete-time system stable for both approximations? (d) Assume that Ts= 0.02. Draw the bode plots (using MATLAB) for the original continuous time system and the two approximated systems. Comment on their differences and similarities. [25]