Frequency-domainL₂-stability conditions for switched linear and nonlinear SISO systems

An algorithm to verify asymptotic stability conditions of a certain family of systems of differential equations

“…In the work [19] we admit the possibility to apply the results on stability of the family of systems (1) to study and design of new control strategies for variable speed electric generators, because the dynamic model of doubly-fed induction generators can be expressed as a combination of two problems: the first one refers to the study of the stability of the trivial solution of the switched linear system (1); and the second problem would be consider certain affine perturbation, not time-dependent (see [19]). Otherwise, a very important conclusion presented in [24] is that an interesting phenomenon of the switched systems: fast switching can lead to stability, thereby providing an alternative framework for vibrational stability analysis. Thus, we performed several runs of the algorithm to have evidence of the existence of stable pairs of matrices that ensure the stability of the whole family of systems (1) and with different levels of proximity to the region of instability (trace and determinant zero).…”