Algorithm for constructing counterexamples to the Kalman problem

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Hidden oscillations in dynamical systems (2011, methodology): “Using a smallness of function φ(σ), we can apply and mathematically strictly justify [26, 27, 28, 16, 25, 29] the method of harmonic linearization (describing function method) for the system dx dt = P0x + qφ (rx) (10)”
Hidden oscillations in mathematical model of drilling system actuated by induction motor with a wound rotor (2014, background): “, localization of hidden oscillations in various modifications of electrical Chua circuits [33,34,36,50–52], counterexamples to Aizerman conjecture and Kalman conjecture on absolute stability of nonlinear control systems [35,44,45], phase-locked loops [48,49], and aircraft control systems [5,6].”
Hidden attractor in smooth Chua systems (2012, background): “In the 50–60’s of the last century the investigations of widely known Markus–Yamabe’s [11], Aizerman’s [12], and Kalman’s [13] conjectures on absolute stability, have led to the finding of hidden oscillations in the dynamical model of automatic control systems with scalar piecewise-linear nonlineari”
Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua’s circuits (2011, methodology): “Algorithm 1. We set up a computational procedure for the sequence of nonlinearities as follows [55, 56 ]”