Semistability theory for spatially distributed systems

The concepts of semistability and exponential semistability are well-developed for finite-dimensional systems with nonisolated equilibrium points, where asymptotic or exponential stability is not possible. Definitions of semistability and exponential semistability have recently been formulated for n...

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Bibliographic Details
Published in:Systems & control letters 2013-10, Vol.62 (10), p.862-870
Main Authors: Hui, Qing, Berg, Jordan M.
Format: Article
Language:English
Subjects:
Approximation
Asymptotic properties
Computer networks
Control systems
Networks
Non-isolated equilibrium
Semigroup
Semistability
Spatially distributed systems
Stability
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Summary:The concepts of semistability and exponential semistability are well-developed for finite-dimensional systems with nonisolated equilibrium points, where asymptotic or exponential stability is not possible. Definitions of semistability and exponential semistability have recently been formulated for networks with time-delays. This paper further extends the semistability theory to continuous and discrete spatially distributed systems. This requires the definition of the notions of exact and approximate semicontrollability and semiobservability, and discrete approximate semicontrollability and semiobservability. Also introduced is the property of weak semistability. Necessary and sufficient conditions are given for exponential semistability and weak semistability, and sufficient conditions are given for semistability.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2013.06.016