### Abstract

This paper gives a solution to the problem of verifying stability of networks consisting of integral input-to-state stable (iISS) subsystems. The iISS small-gain theorem developed recently has been restricted to interconnection of two subsystems. For large-scale systems, stability criteria relying only on gain-type information have been successful only in dealing with input-to-state stable stable (ISS) subsystems. To address the stability problem involving iISS subsystems interconnected in general structure, this paper shows how to construct Lyapunov functions of the network by means of nonlinear sum of individual Lyapunov functions of subsystems given in a dissipation formulation under an appropriate small-gain condition.

Original language | English (US) |
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Title of host publication | Proceedings of the 2011 American Control Conference, ACC 2011 |

Pages | 1971-1977 |

Number of pages | 7 |

State | Published - 2011 |

Event | 2011 American Control Conference, ACC 2011 - San Francisco, CA, United States Duration: Jun 29 2011 → Jul 1 2011 |

### Other

Other | 2011 American Control Conference, ACC 2011 |
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Country | United States |

City | San Francisco, CA |

Period | 6/29/11 → 7/1/11 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*Proceedings of the 2011 American Control Conference, ACC 2011*(pp. 1971-1977). [5991069]

**A small-gain theorem and construction of sum-type Lyapunov functions for networks of iISS systems.** / Ito, Hiroshi; Jiang, Zhong-Ping; Dashkovskiy, Sergey N.; Ruffer, Björn S.

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

*Proceedings of the 2011 American Control Conference, ACC 2011.*, 5991069, pp. 1971-1977, 2011 American Control Conference, ACC 2011, San Francisco, CA, United States, 6/29/11.

}

TY - GEN

T1 - A small-gain theorem and construction of sum-type Lyapunov functions for networks of iISS systems

AU - Ito, Hiroshi

AU - Jiang, Zhong-Ping

AU - Dashkovskiy, Sergey N.

AU - Ruffer, Björn S.

PY - 2011

Y1 - 2011

N2 - This paper gives a solution to the problem of verifying stability of networks consisting of integral input-to-state stable (iISS) subsystems. The iISS small-gain theorem developed recently has been restricted to interconnection of two subsystems. For large-scale systems, stability criteria relying only on gain-type information have been successful only in dealing with input-to-state stable stable (ISS) subsystems. To address the stability problem involving iISS subsystems interconnected in general structure, this paper shows how to construct Lyapunov functions of the network by means of nonlinear sum of individual Lyapunov functions of subsystems given in a dissipation formulation under an appropriate small-gain condition.

AB - This paper gives a solution to the problem of verifying stability of networks consisting of integral input-to-state stable (iISS) subsystems. The iISS small-gain theorem developed recently has been restricted to interconnection of two subsystems. For large-scale systems, stability criteria relying only on gain-type information have been successful only in dealing with input-to-state stable stable (ISS) subsystems. To address the stability problem involving iISS subsystems interconnected in general structure, this paper shows how to construct Lyapunov functions of the network by means of nonlinear sum of individual Lyapunov functions of subsystems given in a dissipation formulation under an appropriate small-gain condition.

UR - http://www.scopus.com/inward/record.url?scp=80053157731&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053157731&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:80053157731

SN - 9781457700804

SP - 1971

EP - 1977

BT - Proceedings of the 2011 American Control Conference, ACC 2011

ER -