Design of exponential stabilizing controller for open-loop unstable bilinear systems

The previous research on the quadratic stabilizing controller for bilinear systems mainly focuses on those systems with (neutrally) stable open-loop dynamics. When the open-loop dynamics is unstable, these quadratic controllers only show the ability of bringing the system states to a bounded region around the origin. To drive the state of an open-loop unstable system to the origin exponentially, we propose a new nonlinear controller design in this paper. By slight modification, this nonlinear control algorithm can be extended to time varying bilinear systems.