Singular PDE's and the single-step formulation of feedback linearization with pole-placement

Abstract

The paper proposes a new formulation to the feedback linearization problem. The problem under consideration is formulated in the context of singular PDE theory. In particular, the mathematical formulation of the problem is realized via a system of first-order quasi-linear singular PDEs, and a rather general set of necessary and sufficient conditions for solvability is derived, by using Lyapunov's auxiliary theorem on singular PDEs. The solution to the above system of PDEs is locally analytic and this enables the development of a series solution method, that is easily programmable with the aid of a symbolic software package. Under a simultaneous implementation of a nonlinear coordinate transformation and a nonlinear state feedback law computed through the solution of the system of PDEs, both feedback linearization and pole-placement design objectives are accomplished in one step, avoiding the restrictions of the other approaches.