## Abstract

This paper presents a Lyapunov formulation of the small-gain theorem for the finite-time input-to-state stability (FTISS) of an interconnected nonlinear system composed of two or more FTISS subsystems. In addition, an FTISS-Lyapunov function for the interconnected system is constructed from the FTISS-Lyapunov functions of the subsystems. With respect to the previously developed nonlinear, Lyapunov-based small-gain theorem restricted to input-to-state stability, a new power-function-based scaling technique is proposed to deal with the challenge that a nonlinearly scaled FTISS-Lyapunov function may not retain a decreasing rate as a power function with a positive power less than one.

Original language | English (US) |
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Pages (from-to) | 1-8 |

Number of pages | 8 |

Journal | IEEE Transactions on Automatic Control |

DOIs | |

State | Accepted/In press - 2023 |

## Keywords

- Finite-time input-to-state stability
- Interconnected systems
- Large-scale systems
- Lyapunov methods
- Nonlinear systems
- Stability criteria
- Standards
- Trajectory
- lyapunov functions
- small-gain theorem

## ASJC Scopus subject areas

- Control and Systems Engineering
- Computer Science Applications
- Electrical and Electronic Engineering