Output Feedback Stabilization of Nonlinear Feedforward Systems using Low Gain Homogeneous Domination

Abstract

This paper examines the result of an output feedback stabilization method for the control of feedforward homogeneous nonlinear systems with unmeasurable states. The feedforward system is made up of a nominal plant which is described by a chain of odd power integrators and coupled with high order nonlinear functions. These nonlinear functions are assumed to be bounded by functions with homogeneous dilations. By making use of the adding a power integrator technique in combination with homogeneous system theory, an observer and controller is implemented which can compensate for the high order homogeneous functions of the feedforward system using only the measured state. This is accomplished through the use of a low gain scaling factor, which when appropriately chosen, will dominate the high order nonlinearities. The significance of this result is that little information about the nonlinear system is required to stabilize this system.