Passivity and absolute stabilization of a class of discrete-time nonlinear systems

doi:10.1016/0005-1098(94)00075-T

Automatica

Volume 31, Issue 2, February 1995, Pages 263-267

https://doi.org/10.1016/0005-1098(94)00075-T Get rights and content

Abstract

By using the theory of discrete-time passive systems and the concept of feedback equivalence, we present an approach toward deriving sufficient conditions for the global stabilization of discrete-time nonlinear systems in the form x(k + 1) = tf(x(k)) + g(x(k))u(k).

The central feature of the approach is that, a unifying set of stability criteria can be obtained and the stability results recover the previous stabilization schemes proposed in the literature.

References (22)

C.I. Byrnes et al.
Local stabilization of minimum phase nonlinear systems
Syst. Contr. Lett.
(1988)
C.I. Byrnes et al.
New results and examples in nonlinear feedback stabilization
Syst. Contr. Lett.
(1989)
C.I. Byrnes et al.
Stabilization of discrete-time nonlinear systems by smooth state feedback
Syst. Contr. Lett.
(1993)
D. Hill et al.
Stability results for nonlinear feedback systems
Automatica
(1977)
V. Jurdjevic et al.
Controllability and stability
J. Diff. Eq.
(1978)
K.K. Lee et al.
Remarks on smooth feedback stabilization of nonlinear systems
Syst. Contr. Lett.
(1988)
C.I. Byrnes et al.
A frequency domain for nonlinear systems, with application to stabilization and adaptive control
C.I. Byrnes et al.
Asymptotic stabilization of minimum phase nonlinear systems
IEEE Trans. Autom. Contr.
(1991)
C.I. Byrnes et al.
Discrete-time lossless systems, feedback equivalence and passivity
C.I. Byrnes et al.
Losslessness, feedback equivalence and the global stabilization of discrete-time nonlinear systems
IEEE Trans. Autom. Contr.
(1994)

C.I. Byrnes et al.

Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems

IEEE Trans. Autom. Contr.

(1991)

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^☆: This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor Hassan Khalil under the direction of Editor Tamer Başar.

^☆☆: Research supported in part by grants from the AFOSR and NSF.

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Brief paperPassivity and absolute stabilization of a class of discrete-time nonlinear systems☆,☆☆

Abstract

Syst. Contr. Lett.

Syst. Contr. Lett.

Syst. Contr. Lett.

Automatica

J. Diff. Eq.

Syst. Contr. Lett.

A frequency domain for nonlinear systems, with application to stabilization and adaptive control

Asymptotic stabilization of minimum phase nonlinear systems

IEEE Trans. Autom. Contr.

Discrete-time lossless systems, feedback equivalence and passivity

Losslessness, feedback equivalence and the global stabilization of discrete-time nonlinear systems

IEEE Trans. Autom. Contr.

Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems

IEEE Trans. Autom. Contr.

Brief paper
Passivity and absolute stabilization of a class of discrete-time nonlinear systems☆,☆☆