The expertise of a professional mathmatician and a theoretical engineer provides a fresh perspective of stability and stable oscillations. The current state of affairs in stability theory, absolute stability of control systems, and stable oscillations of both periodic and almost periodic discrete systems is presented, including many applications in engineering such as stability of digital filters, digitally controlled thermal processes, neurodynamics, and chemical kinetics. This book will be an invaluable reference source for those whose work is in the area of discrete dynamical systems, difference equations, and control theory or applied areas that use discrete time models.
Part I: Introduction 1. Models with Discrete Storage of the Information 2. Discrete-Time Models Induced by Impulses Occurring in Continous Time Systems 3. Discrete Systems Occourring from Sampled Data Control Systems 4. Numerical Treatment of Continous-Time Systems II: Stability Theory 5. Linear Discrete Time Systems with Constant Coefficients 6. General Properties of Linear Systems 7. Stability by the First Approximation 8. Linear Discrete-Time Systems with Periodic Coefficients 9. Liapunov Functions 10. Invariance Principle. Barbashin-Krasovskii-La Salle Theorem 11. Stability in Discrete Models of Chemical Kinetics 12. Stability Results in Neurodynamics 13. Stability Via Input/Output Properties III: Absolute Stability of Control Systems 14. The Simplist Absolute Stability Criterion of Ya. Z. Tsypkin 15. More Special Classes of Nonlinearities; Quadratic Constraints of Yakubovich Type 16. An Absolute Stability Criterion for the Case of Nondecreasing Nonlinearity 17. The Brockett-Willems Type Criterion for Systems with Nondecreasing Nonlinearity 18. Liapunov Functions and Frequency Domain Inequalities in Absolute Stability. The Lemma of Kalman-Szego-Popov-Yakubovich (Single Input Case) 19. A New Condition of Absolute Stability for Systems with Slope Restricted Nonlinearity 20. The Kalman-Szego-Popov-Yakubovich Result for Multi-Input Systems 21. Absolute Stability Conditions for Systems with Several Nonlinearities IV: Stable Oscillations 22. Periodic Solutions of Forced Linear Systems with Periodic Coefficiencients (Forced Oscillations) 23. Almost Periodic Sequences 24. Forced Almost Periodic Oscillations 25. Linear Systems in a Product Space. Stable Invariant Surfaces 26. Nonlinear Periodic and Almost Periodic Oscillations 27. Invariant Manifolds for Nonlinear Systems in a Product Space 28. Frequency Domain Conditions for Stable Oscillations of Control Systems 4. Stable Oscillations