This book presents a development of the frequency-domain approach to the stability study of stationary sets of systems with discontinuous nonlinearities. The treatment is based on the theory of differential inclusions and the second Lyapunov method. Various versions of the Kalman–Yakubovich lemma on solvability of matrix inequalities are presented and discussed in detail. It is shown how the tools developed can be applied to stability investigations of relay control systems, gyroscopic systems, mechanical systems with a Coulomb friction, nonlinear electrical circuits, cellular neural networks, phase-locked loops, and synchronous machines.

Contents:

• Foundations of Theory of Differential Equations with Discontinuous Right-Hand Sides
• Auxiliary Algebraic Statements on Solutions of Matrix Inequalities of a Special Type
• Dichotomy and Stability of Nonlinear Systems with Multiple Equilibria
• Stability of Equilibria Sets of Pendulum-Like Systems

“This book is well worth acquiring, not only for reading in English V A Yakubovich explaining the topics which made him famous, but also as a reference for results when this area is extended to differential inclusions.”

“... there are many interesting comments and pointers to references concerned with the history of the subject. The main results presented were original contributions of the authors. All topics are closely related to the problem of stability analysis of systems having discontinuous nonlinearities, based on frequency-domain methods ... The reviewer recommends this book: first, to mathematicians interested in control theory and, second, to researchers interested in systems having nonsmooth nonlinearities and their technical applications.” (See Full Review)