Detectability, observability and Lyapunov-type theorems of linear discrete time-varying stochastic systems with multiplicative noise

Weihai Zhang; Wei Xing Zheng; Bor-Sen Chen

Detectability, observability and Lyapunov-type theorems of linear discrete time-varying stochastic systems with multiplicative noise

Weihai Zhang, Wei Xing Zheng, Bor-Sen Chen

Western Sydney University

Research output: Contribution to journal › Article › peer-review

27 Citations (Scopus)

Abstract

The objective of this paper is to study detectability, observability and related Lyapunov-type theorems of linear discrete-time time-varying stochastic systems with multiplicative noise. Some new concepts such as uniform detectability, K âˆž -exact detectability (resp. K WFT -exact detectability, K FT -exact detectability, K FT -exact detectability) and K âˆž -exact observability (resp. K WFT -exact detectability, K FT -exact detectability, K N -exact detectability) are introduced, respectively, and nice properties associated with uniform detectability, exact detectability and exact observability are also obtained. Moreover, some Lyapunov-type theorems associated with generalised Lyapunov equations and exponential stability in mean square sense are presented under uniform detectability, K N -exact observability and K N -exact detectability, respectively.

Original language	English
Pages (from-to)	2490-2507
Number of pages	18
Journal	International Journal of Control
Volume	90
Issue number	11
Publication status	Published - 2 Nov 2017

Bibliographical note

Publisher Copyright:
© 2016 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

Lyapunov functions
detectability
multiplicative noise
observability
stochastic systems

Cite this

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title = "Detectability, observability and Lyapunov-type theorems of linear discrete time-varying stochastic systems with multiplicative noise",

abstract = "The objective of this paper is to study detectability, observability and related Lyapunov-type theorems of linear discrete-time time-varying stochastic systems with multiplicative noise. Some new concepts such as uniform detectability, K {\^a}ˆ{\v z} -exact detectability (resp. K WFT -exact detectability, K FT -exact detectability, K FT -exact detectability) and K {\^a}ˆ{\v z} -exact observability (resp. K WFT -exact detectability, K FT -exact detectability, K N -exact detectability) are introduced, respectively, and nice properties associated with uniform detectability, exact detectability and exact observability are also obtained. Moreover, some Lyapunov-type theorems associated with generalised Lyapunov equations and exponential stability in mean square sense are presented under uniform detectability, K N -exact observability and K N -exact detectability, respectively.",

keywords = "Lyapunov functions, detectability, multiplicative noise, observability, stochastic systems",

author = "Weihai Zhang and Zheng, {Wei Xing} and Bor-Sen Chen",

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TY - JOUR

T1 - Detectability, observability and Lyapunov-type theorems of linear discrete time-varying stochastic systems with multiplicative noise

AU - Zhang, Weihai

AU - Zheng, Wei Xing

AU - Chen, Bor-Sen

PY - 2017/11/2

Y1 - 2017/11/2

N2 - The objective of this paper is to study detectability, observability and related Lyapunov-type theorems of linear discrete-time time-varying stochastic systems with multiplicative noise. Some new concepts such as uniform detectability, K âˆž -exact detectability (resp. K WFT -exact detectability, K FT -exact detectability, K FT -exact detectability) and K âˆž -exact observability (resp. K WFT -exact detectability, K FT -exact detectability, K N -exact detectability) are introduced, respectively, and nice properties associated with uniform detectability, exact detectability and exact observability are also obtained. Moreover, some Lyapunov-type theorems associated with generalised Lyapunov equations and exponential stability in mean square sense are presented under uniform detectability, K N -exact observability and K N -exact detectability, respectively.

AB - The objective of this paper is to study detectability, observability and related Lyapunov-type theorems of linear discrete-time time-varying stochastic systems with multiplicative noise. Some new concepts such as uniform detectability, K âˆž -exact detectability (resp. K WFT -exact detectability, K FT -exact detectability, K FT -exact detectability) and K âˆž -exact observability (resp. K WFT -exact detectability, K FT -exact detectability, K N -exact detectability) are introduced, respectively, and nice properties associated with uniform detectability, exact detectability and exact observability are also obtained. Moreover, some Lyapunov-type theorems associated with generalised Lyapunov equations and exponential stability in mean square sense are presented under uniform detectability, K N -exact observability and K N -exact detectability, respectively.

KW - Lyapunov functions

KW - detectability

KW - multiplicative noise

KW - observability

KW - stochastic systems

UR - http://handle.westernsydney.edu.au:8081/1959.7/uws:39145

M3 - Article

SN - 0020-7179

VL - 90

SP - 2490

EP - 2507

JO - International Journal of Control

JF - International Journal of Control

IS - 11

ER -

Detectability, observability and Lyapunov-type theorems of linear discrete time-varying stochastic systems with multiplicative noise

Abstract

Bibliographical note

Keywords

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