Stability of Time-Varying Homogeneous Systems With Mixed Delays and Disturbances Through Novel Nonlinear Halanay Inequality

This paper investigates the stability of time-varying homogeneous systems subject to mixed time delays and exogenous disturbances. The primary contributions include: (1) The innovative development of nonlinear Halanay-type differential inequalities that fundamentally extend conventional formulations through (i) the removal of stringent coefficient constraints prevailing in current literature, and (ii) the unification of some existing results under a generalized analytical framework; (2) Establishment of rigorous stability criteria through synergistic integration of the proposed inequalities with nonlinear comparison principles, enabling precise characterization of practical exponential stability and practical polynomial stability; (3) Comprehensive numerical verification, which not only demonstrates remarkable consistency with theoretical predictions but also successfully applies these theoretical findings to address the consensus problem in leader-follower multi-agent networks. These contributions collectively establish a critical linkage between stability theory and engineering applications under complex constraints.