Exponential stabilization of bilinear systems with open-loop unstablo dynamics

The quadratic control (or its modification) can stabilize a homogeneous bilinear system asymptotically (or exponentially) if its open-loop dynamics are neutrally stable. When the open-loop dynamics are unstable, the quadratic control can only bring the system state to a bounded region around the origin. We propose a new nonlinear control which can drive the state of an open-loop unstable system to the origin exponentially. This control algorithm can be easily extended to time varying systems with slight modification.