LMI‐Based Finite‐Time Stability Analysis of Homogeneous Systems With Sector Nonlinearities and Its Applications to Multi‐Agent Control and Observation

ABSTRACT The problem of finite‐time stability analysis for a class of homogeneous systems with sector nonlinearities is addressed. The proposed method broadens the class of admissible systems and simplify the applicability conditions compared to existing approaches. A key advantage is the introduction of a unified framework for stability analysis in various homogeneity‐based applications with sector nonlinearities. Its efficacy is demonstrated by deriving stability conditions for homogeneous observers and designing finite‐time control protocols for second‐order multi‐agent systems, solving the uniform allocation and average consensus problems.