On existence of oscillations in Persidskii systems

The conditions of existence of oscillations in the sense of Yakubovich are considered for a class of generalized nonlinear Persidskii systems. To this end, the conditions of local instability at the origin and global boundedness of solutions are presented in the form of linear matrix inequalities. The proposed theory is applied for robustness analysis of nonlinear feedback controls in linear systems with respect to unmodeled dynamics.