1. The linearized equations of motion for the lateral dynamics of an aircraft are given by, d dt -10 0 -10 0 P -0.7 1 9 0 -0.7 0 1 0 0 0 20 2.8 -3.13 0 0 0 where p and r are incremental roll and yaw rates, is an incremental sideslip angle, and is an incremental roll angle. The control inputs are incremental changes in aileron deflection angle da and rudder deflection angle dr. (a) Confirm that the system is controllable. Will the system remain controllable if either da or r can no longer be actuated? (b) Suppose that a rate gyro is used to measure the roll rate p. Assuming this is the only quantity measured, find the observability matrix for the corresponding system. Is the system observable? (c) Suppose that a bank indicator is used to measure the bank angle . Assuming this is the only quantity measured, find the observability matrix for the corresponding system. Is the system observable?