Stabilization of exponentially unstable linear systems with input nonlinearities and its application

This paper investigates the stabilization problem for unstable linear systems with input nonlinearities. It is shown that the global stabilization problem of the unstable linear systems with input nonlinearities is solvable if the input nonlinear functions satisfy a linear growth condition. The upper bound of the growth ratio relies on the solution of a set of Lyapunov equations. Moreover, the solvability condition can be applied to solve a global stabilization problem for a class of non-minimum phase nonlinear systems in output feedback form.