Simultaneous Quadratic Stabilization for Discrete-Time Nonlinear Systems

A constructive method is developed for designing simultaneously quadratically stabilizing state feedback controllers for a collection of single-input discrete-time nonlinear systems. In the context of quadratic control Lyapunov functions a necessary and sufficient condition for the existence of simultaneously quadratically stabilizing state feedback laws is derived. An explicit formula for constructing continuous simultaneously stabilizing controllers is presented. The obtained results are verified by a numerical example.