The Lyapunov functions determining the necessary and sufficient conditions for absolute stability of nonlinear nostationary control systems. II

For uniform absolute stability of nonlinear control systems with a range of nonstationary nonlinearities that satisfy sector constraints, the existence of a Lyapunov function from the range of even power forms of a special kind is shown to be necessary and sufficient. This result and the findings of the first installment [1] are extended to the case of a totality of linear nonstationary systems whose coefficients can vary within specified intervals in an unknown way. An example is provided of a nonlinear second-order system in which a Lyapunov function is obtained which specifies the entire region of absolute stability for a parameter which determines the class of nonlinearities.