The class of parameter-varying generalized Persidskii systems is introduced. For models within this class, characterized by nonlinearities satisfying the passivity property, the conditions for (integral) input-to-state stability are proposed. These conditions are established using both, parameter-dependent and parameter-independent, Lyapunov functions. To formulate these conditions, parameterized matrix inequalities are used, which can be reduced into linear ones under additional assumptions concerning the model's dependence on scheduling variables. The efficiency of these stability conditions is illustrated through a numerical example.