Formulas relating script K sign ℒ stability estimates of discrete-time and sampled-data nonlinear systems

D. Nešić, A. R. Teel, E. D. Sontag

Research output: Contribution to journalArticlepeer-review

237 Scopus citations

Abstract

We provide an explicit script K sign ℒ stability or input-to-state stability (ISS) estimate for a sampled-data nonlinear system in terms of the script K sign ℒ estimate for the corresponding discrete-time system and a script K sign function describing inter-sample growth. It is quite obvious that a uniform inter-sample growth condition, plus an ISS property for the exact discrete-time model of a closed-loop system, implies uniform ISS of the sampled-data nonlinear system. Our results serve to quantify these facts by means of comparison functions. Our results can be used as an alternative to prove and extend results in [1] or extend some results in [4] to a class of nonlinear systems. Finally, the formulas we establish can be used as a tool for some other problems which we indicate.

Original languageEnglish (US)
Pages (from-to)49-60
Number of pages12
JournalSystems and Control Letters
Volume38
Issue number1
DOIs
StatePublished - Sep 15 1999

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • General Computer Science
  • Mechanical Engineering
  • Electrical and Electronic Engineering

Keywords

  • Discrete-time
  • Input-to-state stability
  • Sampled data
  • Script K sign ℒ functions
  • Stability

Fingerprint

Dive into the research topics of 'Formulas relating script K sign ℒ stability estimates of discrete-time and sampled-data nonlinear systems'. Together they form a unique fingerprint.

Cite this