Uniform asymptotic stability of non-linear singularly perturbed general and large-scale systems

New general advantageous criteria are established for uniform asymptotic stability of singularly perturbed general and large-scale systems possibly containing non-differentiable non-linearities, which often appear in control systems. For systems with multiple time scales caused by several small parameters, or for large-scale systems, an essential order reduction of aggregation matrices is achieved. The results are conceptually and numerically applied to the absolute stability analysis of singularly perturbed Lurie-Postnikov systems.