Observer and output feedback control for nonlinear ordinary differential equation coupled to an under‐actuated transport partial differential equation

Abstract In this article, the under‐actuation problem for a class of first order hyperbolic partial differential equation system coupled to a nonlinear ordinary differential equation is considered. An anticollocated observer design and an appropriate output feedback control is developed based on the backstepping methodology. The stability conditions for the nonlinear coupled system are proposed using the Lyapunov theory and are formulated in terms of the LMI constraints. Further, we have extended the stability results and backstepping control design for the fractional‐order coupled system. The stability conditions and the control law proposed in the work are evaluated considering a numerical simulation.