Problem 1 (15 points) Consider the circuit shown below, assume R, L,C> 0. The state vector is defined as x = the input u is the input voltage and the output is ve. R Ve 1. Find the state space representation of the system. HINT: to generate the dynamics, use the voltage divider equation and impedance. 2. What are the requirements on R, L, C for the system to be stable? 3. Is the system controllable? What are the requirements on R, L, C for the system to be controllable? 4. For R = 29, L = 10H, C = 0.1F, design a feedback system u = -Kx where K = [K1, K2] so that the closed loop system has CCL = 0.8 and w = 2rad/s. 5. Design an observer for the to estimate the state of the system with closed loop poles at -10, -15.