Supplement: Linear Systems Theory

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).

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Contents

Contents and Preface (PDF, 30 Oct 2020) Ch 1 - Signals and Systems (PDF, 30 Oct 2020) Linear Spaces and Mappings Input/Output Dynamical Systems Linear Systems and Transfer Functions System Norms Exercises Ch 2 - Linear Input/Output Systems (PDF, 30 Oct 2020) Matrix Exponential Convolution Equation Linear System Subspaces Input/output stability Time-Varying Systems Exercises Ch 3 - Reachability and Stabilization (PDF, 30 Oct 2020) Concepts and Definitions Reachability for Linear State Space Systems System Norms Stabilization via Linear Feedback Exercises

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)