Exponential stabilization of a constrained bilinear system
The paper deals with single input, finite dimensional bilinear systems of the form \[ \dot x = Ax + uNx. \] The author shows that if the pair \((A,N)\) satisfies a suitable algebraic condition, then the system can be globally and exponentially stabilized at zero by means of a feedback law \(u(x)\) which is discontinuous at the origin and homogeneous of degree zero. Moreover, \(u(x)\) can be chosen in order to meet a preassigned constraint of the form \(|u|\leq u_{\max}\).
scientific article; zbMATH DE number 1325619