Changing supply rates for input–output to state stable discrete-time nonlinear systems with applications

Dina Shona Laila, D. Nešić

Research output: Contribution to journalArticle

39 Citations (Scopus)

Abstract

We present results on changing supply rates for input–output to state stable discrete-time nonlinear systems. Our results can be used to combine two Lyapunov functions, none of which can be used to verify that the system has a certain property, into a new composite Lyapunov function from which the property of interest can be concluded. The results are stated for parameterized families of discrete-time systems that naturally arise when an approximate discrete-time model is used to design a controller for a sampled-data system. We present several applications of our results: (i) a LaSalle criterion for input to state stability (ISS) of discrete-time systems; (ii) constructing ISS Lyapunov functions for time-varying discrete-time cascaded systems; (iii) testing ISS of discrete-time systems using positive semidefinite Lyapunov functions; (iv) observer-based input to state stabilization of discrete-time systems. Our results are exploited in a case study of a two-link manipulator and some simulation results that illustrate advantages of our approach are presented.
Original languageEnglish
Pages (from-to)821-835
JournalAutomatica
Volume39
Issue number5
DOIs
Publication statusPublished - 19 Mar 2003

Fingerprint

Lyapunov functions
Nonlinear systems
Manipulators
Stabilization
Controllers
Composite materials
Testing

Bibliographical note

The full text is currently unavailable on the repository.

Keywords

  • Discrete time
  • Input-to-state stability
  • Lyapunov method
  • Nonlinear control
  • Supply rates

Cite this

Changing supply rates for input–output to state stable discrete-time nonlinear systems with applications. / Laila, Dina Shona; Nešić, D.

In: Automatica, Vol. 39, No. 5, 19.03.2003, p. 821-835.

Research output: Contribution to journalArticle

@article{5e6ee3b83d774db29f456ead87752fa5,
title = "Changing supply rates for input–output to state stable discrete-time nonlinear systems with applications",
abstract = "We present results on changing supply rates for input–output to state stable discrete-time nonlinear systems. Our results can be used to combine two Lyapunov functions, none of which can be used to verify that the system has a certain property, into a new composite Lyapunov function from which the property of interest can be concluded. The results are stated for parameterized families of discrete-time systems that naturally arise when an approximate discrete-time model is used to design a controller for a sampled-data system. We present several applications of our results: (i) a LaSalle criterion for input to state stability (ISS) of discrete-time systems; (ii) constructing ISS Lyapunov functions for time-varying discrete-time cascaded systems; (iii) testing ISS of discrete-time systems using positive semidefinite Lyapunov functions; (iv) observer-based input to state stabilization of discrete-time systems. Our results are exploited in a case study of a two-link manipulator and some simulation results that illustrate advantages of our approach are presented.",
keywords = "Discrete time, Input-to-state stability, Lyapunov method, Nonlinear control, Supply rates",
author = "Laila, {Dina Shona} and D. Nešić",
note = "The full text is currently unavailable on the repository.",
year = "2003",
month = "3",
day = "19",
doi = "10.1016/S0005-1098(03)00055-4",
language = "English",
volume = "39",
pages = "821--835",
journal = "Automatica",
issn = "0005-1098",
publisher = "Elsevier",
number = "5",

}

TY - JOUR

T1 - Changing supply rates for input–output to state stable discrete-time nonlinear systems with applications

AU - Laila, Dina Shona

AU - Nešić, D.

N1 - The full text is currently unavailable on the repository.

PY - 2003/3/19

Y1 - 2003/3/19

N2 - We present results on changing supply rates for input–output to state stable discrete-time nonlinear systems. Our results can be used to combine two Lyapunov functions, none of which can be used to verify that the system has a certain property, into a new composite Lyapunov function from which the property of interest can be concluded. The results are stated for parameterized families of discrete-time systems that naturally arise when an approximate discrete-time model is used to design a controller for a sampled-data system. We present several applications of our results: (i) a LaSalle criterion for input to state stability (ISS) of discrete-time systems; (ii) constructing ISS Lyapunov functions for time-varying discrete-time cascaded systems; (iii) testing ISS of discrete-time systems using positive semidefinite Lyapunov functions; (iv) observer-based input to state stabilization of discrete-time systems. Our results are exploited in a case study of a two-link manipulator and some simulation results that illustrate advantages of our approach are presented.

AB - We present results on changing supply rates for input–output to state stable discrete-time nonlinear systems. Our results can be used to combine two Lyapunov functions, none of which can be used to verify that the system has a certain property, into a new composite Lyapunov function from which the property of interest can be concluded. The results are stated for parameterized families of discrete-time systems that naturally arise when an approximate discrete-time model is used to design a controller for a sampled-data system. We present several applications of our results: (i) a LaSalle criterion for input to state stability (ISS) of discrete-time systems; (ii) constructing ISS Lyapunov functions for time-varying discrete-time cascaded systems; (iii) testing ISS of discrete-time systems using positive semidefinite Lyapunov functions; (iv) observer-based input to state stabilization of discrete-time systems. Our results are exploited in a case study of a two-link manipulator and some simulation results that illustrate advantages of our approach are presented.

KW - Discrete time

KW - Input-to-state stability

KW - Lyapunov method

KW - Nonlinear control

KW - Supply rates

U2 - 10.1016/S0005-1098(03)00055-4

DO - 10.1016/S0005-1098(03)00055-4

M3 - Article

VL - 39

SP - 821

EP - 835

JO - Automatica

JF - Automatica

SN - 0005-1098

IS - 5

ER -