Stabilizability and identification of systems with one or two unstable poles is addressed. Two limit points of conditional stability are characterized using closed-loop dynamics with a relay and a novel nonlinear element. An algorithm is developed to analyze information from the resultant stable limit cycles in the process input and output. An easily tuned cascade PID control structure is then proposed to stabilize the system and achieve desirable performance. The proposed autotuning technique is tested with good results on a wide variety of unstable systems.