This book investigates the stability of stationary sets in control systems characterized by discontinuous nonlinearities. The authors develop a frequency-domain approach, grounded in the theory of differential inclusions and the second Lyapunov method, to analyze these complex systems. It details various versions of the Kalman-Yakubovich lemma concerning matrix inequalities and demonstrates their application to diverse systems, including relay control, gyroscopic systems, mechanical systems with Coulomb friction, nonlinear electrical circuits, cellular neural networks, phase-locked loops, and synchronous machines.

This technical monograph is likely to be regarded as a significant contribution to the field of control theory, particularly for researchers and advanced students dealing with systems exhibiting discontinuous nonlinearities. The detailed treatment of the Kalman-Yakubovich lemma and its applications suggests a rigorous and comprehensive approach. The breadth of applications discussed indicates the wide relevance of the developed methodologies across various engineering disciplines.