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The lp Induced Norm and the Small-Gain Theorem for Discrete-time Stochastic Systems
- Source :
- ECC
- Publication Year :
- 2018
- Publisher :
- IEEE, 2018.
-
Abstract
- This paper discusses $l_{p}$ induced norms and a small-gain theorem for discrete-time stochastic systems. The induced norm of systems generally depends on the associated input space of the systems. At the beginning, we consider a general stochastic $l_{p}$ space and introduce the primitive $l_{p}$ induced norm based on the space. However, the primitive $l_{p}$ induced norm can actually be confirmed not to reflect the nature of the randomness behind the stochastic systems, which leads us to overestimating its value. Hence, we take a proper subspace of the stochastic $l_{p}$ space and introduce another $l_{p}$ induced norm based on the subspace. We demonstrate with examples that the norm based on the subspace successfully reflects the nature of the system randomness. Then, we give the small-gain theorem based on the norm.
- Subjects :
- 0209 industrial biotechnology
Pure mathematics
Stochastic process
020208 electrical & electronic engineering
02 engineering and technology
Small-gain theorem
020901 industrial engineering & automation
Discrete time and continuous time
Aerospace electronics
0202 electrical engineering, electronic engineering, information engineering
Norm (social)
Randomness
Subspace topology
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- 2018 European Control Conference (ECC)
- Accession number :
- edsair.doi...........c5f1b949cccd83acf3a8c69db3439f3a