| Preface | p. xiii |
| Basic Mathematical Background | p. 1 |
| Introduction | p. 1 |
| Vector Space | p. 1 |
| Normed Space | p. 2 |
| Banach Space | p. 6 |
| Hilbert Space | p. 7 |
| Special Banach Spaces | p. 9 |
| Metric Space | p. 16 |
| Banach Fixed Point Theorems | p. 22 |
| Bibliographical Notes | p. 28 |
| Linear Systems | p. 29 |
| Introduction | p. 29 |
| Some Examples | p. 30 |
| Representation of Solutions for TIS | p. 36 |
| Representation of Solutions for TVS | p. 43 |
| Continuous Dependence of Solution on Data | p. 51 |
| Input-Output Stability and System Equivalence | p. 54 |
| Impulsive (Measure Driven) Systems | p. 63 |
| Systems Subject to Impulsive Inputs | p. 64 |
| Systems Subject to Impulsive Structural Perturbation | p. 67 |
| Controlled Impulsive Systems | p. 72 |
| Exercises | p. 73 |
| Bibliographical Notes | p. 74 |
| Nonlinear Systems | p. 77 |
| Introduction | p. 77 |
| Some Examples | p. 77 |
| Existence and Uniqueness of Solutions | p. 79 |
| Properties of Solution Operator | p. 87 |
| Continuous Dependence of Solutions | p. 89 |
| Impulsive Systems | p. 94 |
| Classical Models | p. 95 |
| General Impulsive Models (Driven by Vector Measures) | p. 102 |
| Differential Inclusions | p. 108 |
| Exercises | p. 115 |
| Bibliographical Notes | p. 116 |
| Basic Stability Theory | p. 119 |
| Introduction | p. 119 |
| Stability of the Equilibrium | p. 120 |
| Lyapunov Stability Theory | p. 124 |
| Lyapunov First Method | p. 133 |
| Stability of Elementary Impulsive Systems | p. 140 |
| Exercises | p. 148 |
| Bibliographical Notes | p. 150 |
| Observability and Identification | p. 151 |
| Introduction | p. 151 |
| Linear Time Invariant Systems | p. 151 |
| Some Examples | p. 159 |
| Linear Time Varying Systems | p. 162 |
| Input Identification | p. 167 |
| Exercises | p. 178 |
| Bibliographical Notes | p. 179 |
| Controllability and Stabilizability | p. 181 |
| Introduction | p. 181 |
| Linear Time Invariant Systems | p. 181 |
| Linear Time Varying Systems | p. 194 |
| Perturbed (Linear/Nonlinear) Systems | p. 200 |
| Stabilizability and Dynamic Compensators | p. 208 |
| Controllability of Linear Impulsive Systems | p. 215 |
| Exercises | p. 218 |
| Bibliographical Notes | p. 219 |
| Basic Calculus of Variations | p. 221 |
| Introduction | p. 221 |
| Finite Dimensional Problems | p. 221 |
| Existence of Solutions for Variational Problems | p. 224 |
| Necessary Conditions | p. 238 |
| Basic Algorithm for Numerical Computation | p. 246 |
| Some Examples | p. 248 |
| Exercises | p. 252 |
| Bibligraphical Notes | p. 253 |
| Optimal Control: Necessary Conditions and Existence | p. 255 |
| Introduction | p. 255 |
| General Problem | p. 255 |
| Necessary Conditions of Optimality | p. 257 |
| Ordinary Controls | p. 257 |
| Transversality Conditions | p. 267 |
| Relaxed Controls | p. 271 |
| Some Special Cases involving constraints | p. 280 |
| Basic Algorithm for Numerical Computation | p. 283 |
| Existence of Optimal Controls | p. 285 |
| Ordinary Controls | p. 285 |
| Relaxed Controls | p. 290 |
| Uncertain Systems/Differential Inclusions | p. 293 |
| Impulsive Controls | p. 297 |
| Exercises | p. 299 |
| Bibliographical Notes | p. 301 |
| Linear Quadratic Regulator Theory | p. 303 |
| Introduction | p. 303 |
| Linear Quadratic Regulator | p. 304 |
| Perturbed Regulators | p. 312 |
| Constrained Regulators | p. 314 |
| Algebraic Riccati Equation: Steady State | p. 316 |
| Some Nonstandard Regulator Problems | p. 320 |
| Disturbance Rejection Problem | p. 328 |
| Structurally Perturbed Impulsive Systems | p. 330 |
| Exercises | p. 335 |
| Bibliographical Notes | p. 335 |
| Time Optimal Control | p. 337 |
| Introduction | p. 337 |
| General Problem | p. 337 |
| Attainable and Reachable Sets | p. 338 |
| Linear Systems | p. 338 |
| Bang-Bang Control | p. 343 |
| Linear Impulsive Systems | p. 348 |
| Nonlinear Systems Including an Algorithm | p. 350 |
| Exercises | p. 356 |
| Bibliographical Notes | p. 357 |
| Stochastic Systems with Applications | p. 359 |
| Introduction | p. 359 |
| Stochastic Systems | p. 359 |
| SDE Based on Brownian Motion | p. 360 |
| SDE Based on Fractional Brownian Motion | p. 369 |
| Differential Equations Based on Poisson Process | p. 373 |
| Application to Auto-Insurance | p. 377 |
| Application to Portfolio Management | p. 379 |
| Population Dynamics | p. 382 |
| Applications to Computer Network | p. 383 |
| Dynamic Model for Access Control | p. 384 |
| TCP Flow Control and Active Queue Management | p. 390 |
| Real Time Control and Optimization | p. 398 |
| Deterministic System | p. 398 |
| Stochastic System | p. 400 |
| Exercises | p. 402 |
| Bibliographical Notes | p. 403 |
| Basic Results from Analysis | p. 405 |
| Introduction | p. 405 |
| Measures and Measurable Functions | p. 405 |
| Riemann and Riemann-Stieltjes Integral | p. 407 |
| Lebesgue Integral | p. 408 |
| Modes of Convergence | p. 411 |
| Frequently Used Results from Measure Theory | p. 414 |
| Frequently Used Results from Analysis | p. 423 |
| Bibliographical Notes | p. 427 |
| Bibliography | p. 429 |
| Index | p. 447 |
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