### Abstract

In this work, we present generalizations of the nonlinear ISS small-gain theorem for discrete-time large-scale systems consisting of multiple subsystems, in a general setting of input-to-output stability. In other words, these discrete-time, large-scale small-gain theorems are established in terms of several types of gain functions, such as asymptotic gains, gains in decay estimations of the output functions, and Lyapunov gains. As a result, the set of cyclic small-gain conditions recovers the case of previously developed small-gain theorems either for an interconnected system comprised of two subsystems, or a network of ISS systems.

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

Title of host publication | Proceedings of the 27th Chinese Control Conference, CCC |

Pages | 704-708 |

Number of pages | 5 |

DOIs | |

State | Published - 2008 |

Event | 27th Chinese Control Conference, CCC - Kunming, Yunnan, China Duration: Jul 16 2008 → Jul 18 2008 |

### Other

Other | 27th Chinese Control Conference, CCC |
---|---|

Country | China |

City | Kunming, Yunnan |

Period | 7/16/08 → 7/18/08 |

### Fingerprint

### Keywords

- Discrete-time systems
- IOS
- ISS ("input-to-state stability")
- Large-scale systems
- Nonlinear small-gain

### ASJC Scopus subject areas

- Control and Systems Engineering

### Cite this

*Proceedings of the 27th Chinese Control Conference, CCC*(pp. 704-708). [4605053] https://doi.org/10.1109/CHICC.2008.4605053

**Nonlinear small-gain theorems for discrete-time large-scale systems.** / Jiang, Zhong-Ping; Lin, Yuandan; Wang, Yuan.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 27th Chinese Control Conference, CCC.*, 4605053, pp. 704-708, 27th Chinese Control Conference, CCC, Kunming, Yunnan, China, 7/16/08. https://doi.org/10.1109/CHICC.2008.4605053

}

TY - GEN

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

AU - Jiang, Zhong-Ping

AU - Lin, Yuandan

AU - Wang, Yuan

PY - 2008

Y1 - 2008

N2 - In this work, we present generalizations of the nonlinear ISS small-gain theorem for discrete-time large-scale systems consisting of multiple subsystems, in a general setting of input-to-output stability. In other words, these discrete-time, large-scale small-gain theorems are established in terms of several types of gain functions, such as asymptotic gains, gains in decay estimations of the output functions, and Lyapunov gains. As a result, the set of cyclic small-gain conditions recovers the case of previously developed small-gain theorems either for an interconnected system comprised of two subsystems, or a network of ISS systems.

AB - In this work, we present generalizations of the nonlinear ISS small-gain theorem for discrete-time large-scale systems consisting of multiple subsystems, in a general setting of input-to-output stability. In other words, these discrete-time, large-scale small-gain theorems are established in terms of several types of gain functions, such as asymptotic gains, gains in decay estimations of the output functions, and Lyapunov gains. As a result, the set of cyclic small-gain conditions recovers the case of previously developed small-gain theorems either for an interconnected system comprised of two subsystems, or a network of ISS systems.

KW - Discrete-time systems

KW - IOS

KW - ISS ("input-to-state stability")

KW - Large-scale systems

KW - Nonlinear small-gain

UR - http://www.scopus.com/inward/record.url?scp=52449095225&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=52449095225&partnerID=8YFLogxK

U2 - 10.1109/CHICC.2008.4605053

DO - 10.1109/CHICC.2008.4605053

M3 - Conference contribution

AN - SCOPUS:52449095225

SN - 9787900719706

SP - 704

EP - 708

BT - Proceedings of the 27th Chinese Control Conference, CCC

ER -