The present work proposes a new formulation to the feedback linearization problem. The problem under consideration is not treated within the context of geometric exact feedback linearization, where restrictive conditions arise, but is conveniently 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 PDE's and a rather general set of necessary and sufficient conditions for solvability is derived, by using Lyapunov's auxiliary theorem on singular PDE's. The solution to the above system of singular PDE's is locally analytic and this enables a series solution method, which 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 PDE's, both feedback linearization and pole-placement design objectives are accomplished in one step, avoiding the restrictions of the other approaches.
Connect With Us: