Nonlinear control design for open-loop unstable quadratic discrete-time systems

This paper deals with the problem of local stabilization, with a guaranteed stability domain and performance, of open-loop unstable quadratic discrete-time systems. For some polyhedral region of the state-space containing the origin, a method is derived for designing a nonlinear static state feedback controller that ensures an enlarged stability domain for the closed-loop system. The stabilization method is then extended to ensure a quadratic performance for a set of admissible initial states. The controller designs are tailored via finite sets of state-dependent linear matrix inequalities. Numerical examples are presented to illustrate the proposed control designs.