Some New Criteria on pth Moment Stability of Stochastic Functional Differential Equations With Markovian Switching

被引：83

作者：

Peng, Shiguo ^{[1
]}

Zhang, Yun ^{[1
]}

机构：

[1] Guangdong Univ Technol, Fac Automat, Guangzhou 510006, Guangdong, Peoples R China

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2010年 / 55卷 / 12期

基金：

中国国家自然科学基金;

关键词：

Markovian switching; pth moment stability; Razumikhin-type theorem; stochastic functional differential equations (SFDEs); RAZUMIKHIN-TYPE THEOREMS; DELAY INTERVAL SYSTEMS; EXPONENTIAL STABILITY; RETARDED-SYSTEMS; JUMP;

D O I：

10.1109/TAC.2010.2074251

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This note gives some new Razumikhin-type theorems on pth moment stability of stochastic functional differential equations with Markovian switching (SFDEwMS) by using auxiliary ordinary differential equation. The main results of this note allow the diffusion operator associated with the underlying SFDEwMS of the Lyapunov function along a solution of the system to be not always negative. An example is provided to illustrate the effectiveness of the proposed results.

引用

页码：2886 / 2890

页数：5

共 20 条

[1] Stability of a random diffusion with linear drift [J].

Basak, GK ;

Bisi, A ;

Ghosh, MK .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1996, 202 (02) :604-622

[2] On delay-dependent stability for a class of nonlinear stochastic systems with multiple state delays [J].

Basin, Michael ;

Rodkina, Alexandra .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (08) :2147-2157

[3] Razumikhin-type theorems on stability of neutral stochastic functional differential equations [J].

Huang, Lirong ;

Deng, Feiqi .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2008, 53 (07) :1718-1723

[4] Razumikhin-type theorems on stability of stochastic retarded systems [J].

Huang, Lirong ;

Deng, Feiqi .

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 2009, 40 (01) :73-80

[5] On Input-to-State Stability of Stochastic Retarded Systems With Markovian Switching [J].

Huang, Lirong ;

Mao, Xuerong .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2009, 54 (08) :1898-1902

[6] Stability of Hybrid Stochastic Retarded Systems [J].

Huang, Lirong ;

Mao, Xuerong ;

Deng, Feiqi .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2008, 55 (11) :3413-3420

[7] Razumikhin-type exponential stability criteria of neutral stochastic functional differential equations [J].

Jankovic, Svetlana ;

Randjelovic, Jelena ;

Jovanovic, Miljana .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 355 (02) :811-820

[8] CONTROLLABILITY, STABILIZABILITY, AND CONTINUOUS-TIME MARKOVIAN JUMP LINEAR QUADRATIC CONTROL [J].

JI, YD ;

CHIZECK, HJ .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1990, 35 (07) :777-788

[9]

Mao X., 2007, Stochastic Differential Equations and Applications, V2nd, DOI DOI 10.1533/9780857099402

[10]

Mao X., 1999, Funct. Differ. Equ., V6, P375

← 1 2 →