Dwell time

Quantum mechanics

Control (management)

Pure mathematics

Discrete mathematics

Exponential stability

Applied mathematics

Stability (learning theory)

Homogeneous polynomial

Computer science

Polynomial

Routh–Hurwitz stability criterion

Contraction (grammar)

Physics

Nonlinear system

Homogeneous

Mathematics

Alternating polynomial

Matrix polynomial

Lyapunov function

Internal medicine

Mathematical analysis

Artificial intelligence

Stable polynomial

Combinatorics

Logarithm

Medicine

Clinical psychology

Control theory (sociology)

Piecewise

Machine learning

Applied Mathematics and Computation

In this article the polynomial stability for positive switching homogeneous systems with different degrees is investigated by proposing a logarithm contraction average dwell-time method. By introducing a class of logarithm contraction average dwell-time switching signals and a piecewise maximum Lyapunov function, we establish an explicit criterion for global polynomial stability of positive switching homogeneous systems whose degrees are greater than one. Especially, the main result is applicable to polynomial stability of Persidskii-type switching systems and consensus of multi-agent systems.

Polynomial stability of positive switching homogeneous systems with different degrees