Supplement: Linear Systems Theory

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Richard M. Murray

These notes serve as a supplement to Feedback Systems by Åström and Murray and expand on some of the topics introduced there. The focus in on more advanced presentations of the material on linear systems, providing a more theory-based coverage of the topics. Each chapter is intended to augment the introductory topics that are introduced in Feedback Systems.

Note: These notes are in draft form and may contain errors. Permission is granted to use and modify these notes for non-commercial purposes provided that appropriate credit is given to the original author and that all modifications contain these same terms (CC-BY-NC-SA).



  • Ch 4 - Optimal Control (PDF, 30 Oct 2020)
    • Review: Optimization
    • Optimal Control of Systems
    • Examples
    • Linear Quadratic Regulators
    • Choosing LQR Weights
    • Advanced Topics
    • FurtherReading
  • Ch 5 - State Estimation (PDF, 30 Oct 2020)
    • Concepts and Definitions
    • Observability for Linear State Space Systems
    • Combining Estimation and Control
    • Exercises
  • Bibliography and Index (PDF, 30 Oct 2020)