Limit of absolute stability of nonlinear nonstationary systems and its connection with the construction of invariant functions (Q1175893)

The absolute stability problem is considered for a class of nonstationary systems. The study is focused on the critical value of the parameter restricting the magnitude of the control signal in the absolute stability characterization of such systems. The critical value is defined as the supremum of the parameter values for which the system in question is absolutely stable. By using variational methods, it is proved that for the parameter critical value, there is a positive convex function whose value along the extremal trajectories of the system is kept constant. The proof of existence of such a function is constructive in that it also provides a test for absolute stability.