A computational approach to approximate input/state feedback linearization

We propose a novel computational approach to the approximate input/state feedback linearization problem by interpolating a finite number of local linear coordinate transforms and static state feedback designs. For a class of single-input nonlinear systems, the approximate approach allows the main assumptions underlying exact input/state feedback linearization (involutivity, smoothness and controllability everywhere) to be relaxed. Moreover, the present approach relies only on simple numeric linear algebraic computations, in strong constrast to the exact input/state feedback linearization approach that relies on the solution of a partial differential equation and other symbolic compuations. In contrast to related approaches to approximation feedback linearization, the feedback design need not be restricted to a neighborhood of the equilibrium manifold. It is shown that the approximation error goes to zero uniformly as the resolution of the state space partitioning increases. Explicit expressions for the approximation error allows the accuracy and robustness of the design to be assessed.