Editing Controllability (section)

== Controllability under input constraints ==

In systems with limited control authority, it is often no longer possible to move any initial state to any final state inside the controllable subspace. This phenomenon is caused by constraints on the input that could be inherent to the system (e.g. due to saturating actuator) or imposed on the system for other reasons (e.g. due to safety-related concerns). The controllability of  systems with input and state constraints is studied in the context of [[reachability (controls)|reachability]]<ref>{{cite journal  |author1=Claire J. Tomlin |author2=Ian Mitchell |author3=Alexandre M. Bayen |author4=Meeko Oishi|author4-link=Meeko Oishi | title = Computational Techniques for the Verification of Hybrid Systems  | journal = Proceedings of the IEEE |volume=91 |issue=7 |pages=986–1001 | doi = 10.1109/jproc.2003.814621 | year = 2003  | url = http://www.cs.ubc.ca/~mitchell/Papers/publishedIEEEproc03.pdf  | access-date = 2012-03-04
|citeseerx=10.1.1.70.4296 }}</ref>  and [[viability theory]].<ref>{{cite book|author=Jean-Pierre Aubin |title= Viability Theory |year=1991 |publisher=Birkhauser |isbn=978-0-8176-3571-8 }}</ref>