### Abstract

This paper presents nonlinear small-gain theorems for input-to-state stability and input-to-output stability properties of large-scale time-delay systems consisting of multiple subsystems based on Razumikhin-type techniques. A key strategy is to follow the spirit of the Razumikhin theorem and treat the state variables with delays as disturbances to the system in question. A consequence of this approach is that the problem of stability analysis for large-scale systems described by functional differential equations is converted into a more tractable one for state-delay-free systems with disturbances.

Original language | English (US) |
---|---|

Pages (from-to) | 27-63 |

Number of pages | 37 |

Journal | Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis |

Volume | 19 |

Issue number | 1 |

State | Published - 2012 |

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### Keywords

- Input-to-output stability
- Input-to-state stability
- Nonlinear small-gain
- Razumikhin theorems
- Time-delay systems

### ASJC Scopus subject areas

- Applied Mathematics
- Analysis
- Discrete Mathematics and Combinatorics

### Cite this

*Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis*,

*19*(1), 27-63.

**Nonlinear small-gain theorems for large-scale time-delay systems.** / Tiwari, Shanaz; Wang, Yuan; Jiang, Zhong-Ping.

Research output: Contribution to journal › Article

*Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis*, vol. 19, no. 1, pp. 27-63.

}

TY - JOUR

T1 - Nonlinear small-gain theorems for large-scale time-delay systems

AU - Tiwari, Shanaz

AU - Wang, Yuan

AU - Jiang, Zhong-Ping

PY - 2012

Y1 - 2012

N2 - This paper presents nonlinear small-gain theorems for input-to-state stability and input-to-output stability properties of large-scale time-delay systems consisting of multiple subsystems based on Razumikhin-type techniques. A key strategy is to follow the spirit of the Razumikhin theorem and treat the state variables with delays as disturbances to the system in question. A consequence of this approach is that the problem of stability analysis for large-scale systems described by functional differential equations is converted into a more tractable one for state-delay-free systems with disturbances.

AB - This paper presents nonlinear small-gain theorems for input-to-state stability and input-to-output stability properties of large-scale time-delay systems consisting of multiple subsystems based on Razumikhin-type techniques. A key strategy is to follow the spirit of the Razumikhin theorem and treat the state variables with delays as disturbances to the system in question. A consequence of this approach is that the problem of stability analysis for large-scale systems described by functional differential equations is converted into a more tractable one for state-delay-free systems with disturbances.

KW - Input-to-output stability

KW - Input-to-state stability

KW - Nonlinear small-gain

KW - Razumikhin theorems

KW - Time-delay systems

UR - http://www.scopus.com/inward/record.url?scp=84863141571&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84863141571&partnerID=8YFLogxK

M3 - Article

VL - 19

SP - 27

EP - 63

JO - Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

JF - Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis

SN - 1201-3390

IS - 1

ER -