Analysis of Singular Perturbations for a Class of Interconnected Homogeneous Systems: Input-to-State Stability Approach⁎This work was supported in part by the Government of Russian Federation (Grant 08-08), by the Ministry of Science and Higher Education of Russian Federation, passport of goszadanie no. 2019-0898; by CONACyT (Consejo Nacional de Cienciay Tecnología) project 241171, 282013 and CVU 711867; by PAPIIT-UNAM (Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica) IN 115419 and IN 113617. Issue 2 (2020) - Mendoza-Avila, Jesús; Efimov, Denis; Moreno, Jaime A.; Fridman, Leonid
Abstract: 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.