A Lyapunov-Based Small-Gain Theorem for a Network of Finite-Time Input-to-State Stable Systems

Huanhuan Li; Tengfei Liu; Zhong Ping Jiang

doi:10.1109/TAC.2023.3274880

A Lyapunov-Based Small-Gain Theorem for a Network of Finite-Time Input-to-State Stable Systems

Huanhuan Li, Tengfei Liu, Zhong Ping Jiang

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

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)
Pages (from-to)	1-8
Number of pages	8
Journal	IEEE Transactions on Automatic Control
DOIs	https://doi.org/10.1109/TAC.2023.3274880
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

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10.1109/TAC.2023.3274880

Cite this

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title = "A Lyapunov-Based Small-Gain Theorem for a Network of Finite-Time Input-to-State Stable Systems",

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.",

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",

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journal = "IEEE Transactions on Automatic Control",

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N1 - Publisher Copyright: IEEE

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - Finite-time input-to-state stability

KW - Interconnected systems

KW - Large-scale systems

KW - Lyapunov methods

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KW - Stability criteria

KW - Standards

KW - Trajectory

KW - lyapunov functions

KW - small-gain theorem

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A Lyapunov-Based Small-Gain Theorem for a Network of Finite-Time Input-to-State Stable Systems

Abstract

Keywords

ASJC Scopus subject areas

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