Finite-Time and Practical Stability of a Class of Stochastic Dynamical Systems

被引：23

作者：

Michel, Anthony N. ^{[1
]}

Hou, Ling ^{[2
]}

机构：

[1] Univ Notre Dame, Dept Elect Engn, Notre Dame, IN 46556 USA

[2] St Cloud State Univ, Dept Elect & Comp Engn, St Cloud, MN USA

来源：

47TH IEEE CONFERENCE ON DECISION AND CONTROL, 2008 (CDC 2008) | 2008年

关键词：

D O I：

10.1109/CDC.2008.4738705

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In practice, one is not only interested in qualitative characterizations provided by Lyapunov and Lagrange stability, but also in quantitative information concerning system behavior, including estimates of trajectory bounds over finite and infinite time intervals. This type of information has been ascertained in a systematic manner using the notions of finite-time stability and practical stability. In the present paper we generalize some of the existing finite-time stability and practical stability results for deterministic dynamical systems determined by ordinary differential equations to dynamical systems determined by an important class of stochastic differential equations. We consider two types of stability concepts: finite-time and practical stability in the mean and in the mean square. We demonstrate the applicability of our results by means of several examples.

引用

页码：3452 / 3456

页数：5

共 12 条

[1]

[Anonymous], 1967, STABILITY MOTION

[2]

Arnold L., 1974, STOCHASTIC DIFFERENT, DOI DOI 10.1002/ZAMM.19770570413

[3]

FENG ZS, 1993, PROCEEDINGS OF THE 32ND IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4, P865, DOI 10.1109/CDC.1993.325023

[4]

Kushner H J., 1967, Stochastic Stability and Control

[5] STABILITY AND TRAJECTORY BEHAVIOR OF COMPOSITE SYSTEMS [J].

MICHEL, AN .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1975, CA22 (04) :305-312

[6] PRACTICAL STABILITY AND FINITE-TIME STABILITY OF DISCONTINUOUS SYSTEMS [J].

MICHEL, AN ;

PORTER, DW .

IEEE TRANSACTIONS ON CIRCUIT THEORY, 1972, CT19 (02) :123-&

[7] QUANTITATIVE ANALYSIS OF SIMPLE AND INTERCONNECTED SYSTEMS - STABILITY, BOUNDEDNESS, AND TRAJECTORY BEHAVIOR [J].

MICHEL, AN .

IEEE TRANSACTIONS ON CIRCUIT THEORY, 1970, CT17 (03) :292-+

[8]

Michel AN, 2008, SYST CONTROL-FOUND A, P1

[9] Practical stability with respect to time-varying sets for stochastic differential systems [J].

Ting, YL .

STOCHASTIC ANALYSIS AND APPLICATIONS, 1999, 17 (05) :895-909

[10] ON STABILITY OF SYSTEMS DEFINED OVER A FINITE TIME INTERVAL [J].

WEISS, L ;

INFANTE, EF .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1965, 54 (01) :44-&

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