Boundary dynamic feedback control for a class of semi-linear distributed parameter systems

The dynamic output feedback control for a class of semi-linear distributed parameter systems with a non-constant (spatially-varying) diffusion rate described by partial differential equations is studied. The considered system is endowed with boundary actuation available and boundary feedback controllers are designed. Meanwhile, both domain-averaged and boundary-valued measurements, two different ways of output measurements, are taken into account. Based on these two different methods of measurements, the corresponding boundary feedback control laws are designed, respectively. Using Wirtinger's inequality, the resulting closed-loop systems depending on observers and controllers are obtained in terms of the Lyapunov method. With the sufficient conditions of the linear matrix inequality, the stability of the system is subsequently obtained by the designed observer and controller. The final numerical simulations are given to illustrate the validity of the results graphically.