- Title
- Complex polytopic Lyapunov functions and componentwise ultimate bounds for switched linear systems: a missing link
- Creator
- Haimovich, Hernan; Vallarella, Alexis J.; Seron, María M.
- Relation
- 2015 XVI Workshop on Information Processing and Control (RPIC). Proceedings of the 2015 XVI Workshop on Information Processing and Control (Cordoba, Argentina 6-9 October, 2015)
- Publisher Link
- http://dx.doi.org/10.1109/RPIC.2015.7497070
- Publisher
- Institute of Electrical and Electronics Engineers (IEEE)
- Resource Type
- conference paper
- Date
- 2016
- Description
- This paper deals with switched linear systems with persistent disturbances and under arbitrary switching. For these systems, a systematic componentwise ultimate bound computation method has been previously developed. This method does not employ a Lyapunov function, yet yields a mixture of ellipsoidal and polyhedral sets, which are the type of level sets obtained via complex polytopic Lyapunov functions. In this context, our contribution is as follows: (a) we show that if the aforementioned componentwise method can be applied, then a complex polytopic Lyapunov function exists based on which the same ultimate bound is obtained; (b) we provide a novel algebraic condition for the existence of a complex polytopic Lyapunov function of minimum complexity; (c) we give an example for which a polytopic Lyapunov function exists but the componentwise method cannot be applied. These results serve to establish the precise connection between the two approaches.
- Subject
- Lyapunov methods; switches; linear systems; complexity theory; stability analysis; context; asymptotic stability
- Identifier
- http://hdl.handle.net/1959.13/1337374
- Identifier
- uon:27826
- Identifier
- ISBN:9781467384667
- Language
- eng
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