Control design for open-loop unstable quadratic systems

This work addresses the problem of designing a state feedback control law for locally stabilizing open-loop unstable quadratic systems with a guaranteed stability domain. Firstly, for some polytopic region of the state-space containing the origin, a method is derived to design a nonlinear static state feedback controller which maximizes the size of the closed-loop system stability domain. Then, the proposed method is extended to handle systems disturbed by energy-bounded signals. The controller designs are tailored via a finite set of state-dependent linear matrix inequalities. Numerical examples are given to illustrate the potentials of the proposed control designs.