Single-step feedback linearization with assignable dynamics for hyperbolic PDE

Abstract

The present work proposes an extension of single-step feedback linearization with pole-placement formulation to the class of nonlinear hyperbolic systems. In particular, the mathematical formulation in the context of singular PDE theory is utilized via system of first order quasi-linear singular PDEs within the nonlinear hyperbolic PDE setting to obtain single step state nonlinear transformation and feedback control law with prescribed closed loop dynamics. The solution of quasi linear singular PDE is guaranteed by the Lyapunov's auxiliary theorem and locally invertible analytic transformation is applied by the full state feedback law to yield desired stable hyperbolic PDE system with assignable dynamics. The simultaneous state transformation and feedback linearization are realized in one step, avoiding the restrictions existing in other approaches.