Stability and Stable Oscillations in Discrete Time Systems

Aristide Halanay, Vladimir Rasvan

• 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