Stabilization and Solution of Two Diminution Nonlinear Hyperbolic Partial Differential Equations Using the Discretized Backstepping Method

Abstract

Stabilizability and solvability of the two – dimensional nonlinear hyperbolic partial differential equation has experienced a growing popularity and of major interest of robust control theory. Therefore, in this paper, the backstepping transformation approach based on discretization of the space variable will be used to study the Stabilizability and solvability of nonlinear two dimensional hyperbolic partial differential equations by transforming the partial differential equation with unknown boundary control in to system of nonlinear ordinary differential equations and then using Lyapunov function method to stabilize and evaluate the control function, while the solution is obtained using Adem-bashforth method.

Keywords: Backstepping method, hyperbolic partial differential equation, Stabilization of boundary control problems, Lyapunov function.