Abstract This work presents the design of a boundary state observer for one-dimensional heterodirectional semilinear hyperbolic partial differential equations. The observer equations are formulated using two correction signals derived from boundary measurements, with one being applied to the source term and another one at the boundaries. To ensure the stability and convergence of the estimation error, sufficient design conditions are derived using Lyapunov theory. These conditions guarantee the exponential stability of the estimation error in the ℒ2 sense, and they are expressed in the form of linear matrix inequalities providing a computational framework for the observer design. A numerical example is presented to validate the proposed methodology.
Carvalho et al. (Wed,) studied this question.