Backstepping observer for distributed parameter systems

In this paper, we design exponentially convergent observer for the systems with distributed parameters. A Volterra integral transformation is used to change the coordinates of the error dynamics into exponentially stable target systems using the backstepping procedure. The gains of the observer, which are attained by solving a Partial Differential Equations (PDE) system with output injection, will guarantee the exponential convergence of the observer. What is more, the design method is applied to a SIR epidemic system to consider the sensitive population.