Algorithms for Searching for Hidden Oscillations in the Aizerman and Kalman Problems

The method of harmonic linearization, describing function method, numerical methods, and the applied bifurcation theory together discover new opportunities for analysis of hidden oscillations of nonlinear control systems. In the present paper new analytical-numerical algorithm for hidden oscillation localization is discussed. Counterexamples construction to Aizerman’s conjecture and Kalman’s conjecture on absolute stability of control systems are considered.