Linear Systems 131 5.1 Basic Definitions 131 5.2 The Matrix Exponential 136 5.3 Input/Output Response 145 5.4 Linearization 158 5.5 Further Reading 163 Exercises 164 Chapter 6. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models.ĭynamic Behavior 95 4.1 Solving Differential Equations 95 4.2 Qualitative Analysis 98 4.3 Stability 102 4.4 Lyapunov Stability Analysis 110 4.5 Parametric and Nonlocal Behavior 120 4.6 Further Reading 126 Exercises 126 Chapter 5. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. Karl Astrom and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. Unlike most books on the subject, Feedback Systems develops transfer functions through the exponential response of a system, and is accessible across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. It is an ideal textbook for undergraduate and graduate students, and is indispensable for researchers seeking a self-contained reference on control theory. This book provides an introduction to the mathematics needed to model, analyze, and design feedback systems.
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