Feedback Linearization of Nonlinear Systems using Generalized Sampled-Data Hold Functions

This paper investigates the use of "Generalized Sampled-Data Hold Functions" (GSHF) in the feedback linearization of analytic nonlinear time-invariant systems. This method uses a state feedback periodic controller in the form of a power series of the state samples x(kT). No coordinate transformation is needed. The idea for linearization is to introduce an i-th order homogeneous polynomial of x(kT) in the feedback to cancel the ith order nonlinearity of the closed loop dynamics. Simple sufficient conditions for the feedback linearization using GSHF controller are obtained. Local convergence of the GSHF feedback law is proven. An example is treated.