This document contains a multi-part exam problem analyzing control systems. Part 1 involves finding the transfer function and difference equation for a system with an impulse response of 1 for the first N points. Part 2 analyzes a continuous-time system with two real poles, one in the right half-plane, and finds its zero-order hold equivalent discrete-time system. The remaining parts involve analyzing the stability of this system using root loci, Nyquist, and designing a lead compensator to stabilize it with over 45 degrees of phase margin.