A harmonic oscillator can be described by the following continuous time, second order system To -4 + 0 y=[o 0.5] a) As a warm-up determine if the continuous time system is observable. (1 p) b) Using zero order hold, discretize the system with sampling time T. (2p) c) Give all possible values of T for which the discrete time system is not ob- servable. Relate this to the result from task a) by showing that the result of a) holds with your solution for the discrete time case. (1 p) d) We do not have access to the states of the system, which means that we only measure the output y. We need an observer to use the states for feedback control. Compute an observer gain K for the discrete time system so that all continuous time poles are located at -1. Consider a sampling time of T = 7/8 (2 p) A harmonic oscillator can be described by the following continuous time, second order system To -4 + 0 y=[o 0.5] a) As a warm-up determine if the continuous time system is observable. (1 p) b) Using zero order hold, discretize the system with sampling time T. (2p) c) Give all possible values of T for which the discrete time system is not ob- servable. Relate this to the result from task a) by showing that the result of a) holds with your solution for the discrete time case. (1 p) d) We do not have access to the states of the system, which means that we only measure the output y. We need an observer to use the states for feedback control. Compute an observer gain K for the discrete time system so that all continuous time poles are located at -1. Consider a sampling time of T = 7/8 (2 p)