Publisher's Synopsis
This book lays the foundation for the study of input-to-state stability (ISS) of partial differential equations (PDEs) predominantly of two classes-parabolic and hyperbolic. This foundation consists of new PDE-specific tools.
In addition to developing ISS theorems, equipped with gain estimates with respect to external disturbances, the authors develop small-gain stability theorems for systems involving PDEs. A variety of system combinations are considered:
- PDEs (of either class) with static maps;
- PDEs (again, of either class) with ODEs;
- PDEs of the same class (parabolic with parabolic and hyperbolic with hyperbolic); and
- feedback loops of PDEs of different classes (parabolic with hyperbolic).
