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This book shows clearly how the study of concrete control systems has motivated the development of the mathematical tools needed for solving such problems. In many cases, by using this apparatus, far-reaching generalizations have been made, and its further development will have an important effect on many fields of mathematics. In the book a way is demonstrated in which the study of the Watt flyball governor has given rise to the theory of stability of motion. The criteria of controllability, observability, and stabilization are stated. Analysis is made of dynamical systems, which describe a

Control theory --- Mathematical models.

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Chaotic behavior in systems. --- Control theory. --- Differentiable dynamical systems. --- Lyapunov stability. --- Stability. --- Stability --- Chaotic behavior in systems --- Control theory --- Lyapunov stability --- Differentiable dynamical systems

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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

Control theory. --- Nonlinear control theory. --- Set theory. --- System analysis. --- Differential equations, Nonlinear. --- Engineering mathematics. --- Engineering systems. --- Engineering --- Engineering analysis --- Mathematical analysis --- Nonlinear differential equations --- Nonlinear theories --- Network analysis --- Network science --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics --- Control theory --- Dynamics --- Machine theory

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Pure sciences. Natural sciences (general)