Semistability theory for spatially distributed systems

At isolated equilibrium points it is appropriate to seek asymptotic or exponential stability. These properties are not possible at non-isolated equilibrium points, and should be replaced by semistability or exponential semistability. These latter notions are well-developed for finite-dimensional systems, and have been extended to systems with time-delay. This paper presents the first extension of semistability theory to spatially distributed systems. Both continuous systems and discrete lattices are considered. Concepts of exact and approximate semicontrollability and semiobservability are developed, and related to a series of semistability tests.