On global stability of quadratic state feedback controlled linear systems

In this article we analyze the global stability of a class of nonlinear system arising from asymptotically stable LTI single input plants controlled by quadratic state feedback. Some requirements on the quadratic feedback gain are given to reduce the possibly negative effect of the quadratic term on the internal stability for second order system. A quadratic state feedback design guideline is presented to improve the initial transient response of the original linear system.