Input-to-state dynamical stability and its Lyapunov function characterization

被引：53

作者：

Grüne, L ^{[1
]}

机构：

[1] Univ Frankfurt, Fachbereich Math, D-60054 Frankfurt, Germany

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2002年 / 47卷 / 09期

关键词：

input-to-state dynamical stability (ISDS); Lyapunov function; nonlinear stability margin; small gain theorem;

D O I：

10.1109/TAC.2002.802761

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We present a new variant of the input-to-state stability (ISS) property which is based on using a one-dimensional dynamical system for building the class KL function for the decay estimate and for describing the influence of the perturbation. We show the relation to the original ISS formulation and describe characterizations by means of suitable Lyapunov functions: As applications, we derive quantitative results on stability margins for nonlinear systems and a quantitative version of a small gain theorem for nonlinear systems.

引用

页码：1499 / 1504

页数：6

共 19 条

[11] Stabilization in spite of matched unmodeled dynamics and an equivalent definition of input-to-state stability
Praly, L
Wang, Y
[J]. MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 1996, 9 (01) : 1 - 33
[12] Remarks regarding the gap between continuous, Lipschitz, and differentiable storage functions for dissipation inequalities appearing in H∞ control
Rosier, L
Sontag, ED
[J]. SYSTEMS & CONTROL LETTERS, 2000, 41 (04) : 237 - 249
[13] Sepulchre R., 1997, Constructive Nonlinear Control
[14] Comments on integral variants of ISS
Sontag, ED
[J]. SYSTEMS & CONTROL LETTERS, 1998, 34 (1-2) : 93 - 100
[15] ON CHARACTERIZATIONS OF THE INPUT-TO-STATE STABILITY PROPERTY
SONTAG, ED
WANG, Y
[J]. SYSTEMS & CONTROL LETTERS, 1995, 24 (05) : 351 - 359
[16] SMOOTH STABILIZATION IMPLIES COPRIME FACTORIZATION
SONTAG, ED
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1989, 34 (04) : 435 - 443
[17] SONTAG ED, NONLINEAR CONTROL YE
[18] On the Input-to-State Stability Property
Sontag, Eduardo D.
[J]. EUROPEAN JOURNAL OF CONTROL, 1995, 1 (01) : 24 - 36
[19] Tsinias J., 1997, ESAIM. Control, Optimisation and Calculus of Variations, V2, P57, DOI 10.1051/cocv:1997103

← 1 2 →