Other PDE-PDE Cascades

Abstract

In this chapter we deal with cascades of parabolic and second-order hyperbolic PDEs. These are example problems. The parabolic-hyperbolic cascade is represented by a heat equation at the input of an antistable wave equation. The hyperbolic-parabolic cascade is represented by a wave equation at the input of an unstable reaction-diffusion equation.

The topic of PDE-PDE cascades is in its infancy. Its comprehensive coverage is beyond the scope of this book. Unlike the previous chapters in this book, our presentation in this chapter is fairly informal. We do derive the feedback laws and make statements of closed-loop eigenvalues; however, we forego a detailed Lyapunov stability analysis and the associated estimates for the transformations between the plant and the target system.