On analysis of Persidskii systems and their implementations using LMIs

The conditions of (integral) input-to-state stability and input-output-to-state stability are established for a class of generalized Persidskii systems. The proposed conditions are formulated using linear matrix inequalities. Based on these results the conditions of convergence are derived for discretizations of this class of models obtained by the explicit and the implicit Euler methods. The proposed theory is finally applied to design a robust stabilization control.