Stability Condition in Terms of the Pole Locations A causal LTI digital filter is BIBO stable if and only if its impulse response h[n] is absolutely summable, i.e., We now develop a stability condition in terms of the pole locations of the transfer function H(z)
1. Studying the Nervous Systems of Humans and Other Animals 1 UNIT I NEURAL SIGNALING 2. Electrical Signals of Nerve Cells 31 3. Voltage-Dependent Membrane Permeability 47 4. Channels and Transporters 69 5. Synaptic Transmission 93 6. Neurotransmitters, Receptors, and Their Effects 129 7. Molecular Signaling within Neurons 165 UNIT II SENSATION AND SENSORY PROCESSING 8. The Somatic Sensory System 189 9. Pain 209 10. Vision: The Eye 229 11. Central Visual Pathways 259 12. The Auditory System 283 13. The Vestibular System 315 14. The Chemical Senses 337 UNIT III MOVEMENT AND ITS CENTRAL CONTROL 15. Lower Motor Neuron Circuits and Motor Control 371 16. Upper Motor Neuron Control of the Brainstem and Spinal Cord 393 17. Modulation of Movement by the Basal Ganglia 417 18. Modulation of Movement by the Cerebellum 435 19. Eye Movements and Sensory Motor Integration 453 20. The Visceral Motor System 469 UNIT IV THE CHANGING BRAIN 21. Early Brain Development 501
1 Introduction 2 Deterministic Dynamic Programming and Viscosity Solutions 2.1 Introduction 2.2 Value Functions are Viscosity Solutions 2.3 Comparison and Uniqueness 3 Stochastic Control 3.1 Some Probability Theory 3.2 Controlled State Space Models 3.3 Filtering 3.4 Dynamic Programming - Case I : Complete State Information 3.5 Dynamic Programming - Case II : Partial State Information 3.6 Two Continuous Time Problems 4 Robust Control 4.1 Introduction and Background 4.2 The Standard Problem of H∞ Control 4.3 The Solution for Linear Systems 4.4 Risk-Sensitive Stochastic Control and Robustness 5 Optimal Feedback Control of Quantum Systems 5.1 Preliminaries 5.2 The Feedback Control Problem 5.3 Conditional Dynamics 5.4 Optimal Control 5.5 Appendix: Formulas for the Two-State System with Feedback Example 6 Optimal Risk-Sensitive Feedback Control of Quantum Systems 6.1 System Model