Analysis of Singular Perturbations for a Class of Interconnected Homogeneous Systems: Input-to-State Stability Approach

In this work an interconnection of two singularly perturbed homogeneous systems of different degrees is considered. Under relaxed restrictions on the smoothness of the right-hand sides of the system, and some standard assumptions, the conditions of local or practical asymptotic stability of the interconnection are established by means of ISS properties and the Small-Gain Theorem. Moreover, the domains of stability and attractions are estimated. Finally, the results are illustrated through an example with a homogeneous system of negative degree.