Zeroing Dynamics‐Based Stabilizing Controller Design of Diffusion‐Reaction Systems

Stabilizing nonlinear distributed parameter systems within the framework of the late lumping approach is a challenging problem. Diffusion‐reaction systems, described by semilinear partial differential equations, represent a common class of distributed parameter systems encountered in real applications. In this work, the zeroing dynamics method is used to design a stabilizing infinite‐dimensional controller for this important class of systems. Both distributed and boundary actuations are investigated. The design of the controller relies on the concept of the characteristic index. In the case of distributed control, as the characteristic index is finite, the design is straightforward. However, in the case of boundary control, the characteristic index is infinite, thus an equivalent pointwise control form is derived to reduce it to a special case of distributed control, which enables the controller design. In the disturbance‐free case, the developed controllers ensure exponential stability. In the presence of disturbances, the closed‐loop system remains stable, and the steady‐state error can be made arbitrarily small by tuning the controller parameters. Four common application examples from the literature are provided to demonstrate the effectiveness of the developed controllers: catalytic rod, monoenzyme system, heated rod, and FitzHugh‐Nagumo equation.