Observer-based feedback stabilization of distributed parameter systems of parabolic type with non-self-adjoint operators

This paper deals with a finite-dimensional feedback stabilization of distributed parameter systems of parabolic type with a non-self-adjoint system operator. When the system operator is self-adjoint as well studied in the previous literature, a finite dimensional feedback stabilizer with a prescribed exponential decay rate can be constructed. It is shown that, even in the case of a non-self-adjoint operator, a similar design method can be applied under some additional assumptions. The controller contains a finite-dimensional observers which can estimate the ill-behaved modes of the plant even under the effect of spillovers.