Please perform the following operations on the given linear-time-invariant system:

O -1 1.5 -0.5 A B 1 -2 C = (1 0], D=0 Input = u(t)*(-1) floor(t), t> 0 a. Check the observability of the system. b. Design an open loop state estimator and: i. Write out the combined state equation. ii. Specify each state matrix and the initial condition of the combined state equation. (Assume your own estimator initial condition that is different from the system one.) C. Design a closed loop state estimator and: i. Find the L that shifts the pole to (-3-4). ii. Write out the combined state equation in system-observer configuration. iii. Write out the combined state equation in system-error configuration. iv. Specify each state matrix and the initial condition of both combined state equations above. (Assume your own estimator initial condition that is different from the system one.) d. Use Matlab to simulate the system with open loop observer. Plot the states of the system and observer. Also plot the errors. e. Use Matlab to simulate the system with close loop observer. Plot the states of the system and observer. Also plot the errors. f. Explain the difference you see in the plots between both estimators. O -1 1.5 -0.5 A B 1 -2 C = (1 0], D=0 Input = u(t)*(-1) floor(t), t> 0 a. Check the observability of the system. b. Design an open loop state estimator and: i. Write out the combined state equation. ii. Specify each state matrix and the initial condition of the combined state equation. (Assume your own estimator initial condition that is different from the system one.) C. Design a closed loop state estimator and: i. Find the L that shifts the pole to (-3-4). ii. Write out the combined state equation in system-observer configuration. iii. Write out the combined state equation in system-error configuration. iv. Specify each state matrix and the initial condition of both combined state equations above. (Assume your own estimator initial condition that is different from the system one.) d. Use Matlab to simulate the system with open loop observer. Plot the states of the system and observer. Also plot the errors. e. Use Matlab to simulate the system with close loop observer. Plot the states of the system and observer. Also plot the errors. f. Explain the difference you see in the plots between both estimators