Controller design for bilinear systems

This note presents an extension of a well-known synthesis technique for linear systems to bilinear plants. A classical quadratic Lyapunov function candidate is first selected. Then the controller is designed so as to make the derivative of that function along the trajectories of the bilinear system as negative as possible. This leads to a bang-bang feedback control law using a nonlinear switching function. It is shown that the closed-loop system is guaranteed to be globally asymptotically stable.