# Dynamic Systems and Control

Written by: Mohammed Dahleh, Munther A. Dahleh and George Verghese (all from MIT)

They are calling this material course notes but they look more like a Dynamic Systems and Control textbook. They are from one of the great MIT open courses in engeineering and computer science. The stated course objectives were:

“The course addresses dynamic systems, i.e., systems that evolve with time. Typically these systems have inputs and outputs; it is of interest to understand how the input affects the output (or, vice-versa, what inputs should be given to generate a desired output). In particular, we will concentrate on systems that can be modeled by Ordinary Differential Equations (ODEs), and that satisfy certain linearity and time-invariance conditions.

We will analyze the response of these systems to inputs and initial conditions. It is of particular interest to analyze systems obtained as interconnections (e.g., feedback) of two or more other systems. We will learn how to design (control) systems that ensure desirable properties (e.g., stability, performance) of the interconnection with a given dynamic system.”

This free online electrical engineering textbook Dynamic Systems and Control are the notes of Mohammed Dahleh, Munther A. Dahleh and George Verghese. All are affiliated with MIT. The chapters are offered as a series of individual PDF files.

This is a graduate-level course. This might not be a complete list but the prerequisites include: Physics II, Signals and Systems course, Linear Algebra, Calculus II, Feedback System Design, Dynamics and Control I and Differential Equations.

Chapter 1: Linear Algebra Review
Chapter 2: Least Squares Estimation
Chapter 3: Least Squares solution of y = < a, x >
Chapter 4: Matrix Norms and Singular Value Decomposition
Chapter 5: Matrix Perturbations
Chapter 6: Dynamic Models
Chapter 7: State-space Models
Chapter 8: Simulation / realization
Chapter 9: (not included in free online text)
Chapter 10: Discrete-time Linear State-space Models
Chapter 11: Continuous-time Linear State-space Models
Chapter 12: Modal Decompostion of State-space Models
Chapter 13: Internal (Lyapunov) Stability
Chapter 14: Internal Stability for LTI Systems
Chapter 15: External Input-output Stability
Chapter 16: (not included in free online text)
Chapter 17: Interconnected Systems and Feedback: Well-posedness, Stability, and Performance
Chapter 18: Performance of Feedback Systems
Chapter 19: Robust Stability in SISO Systems
Chapter 20: Stability Robustness
Chapter 21: Robust Performance and Introduction to the Structured Singular Value Function
Chapter 22: Reachability of DT LTI Systems
Chapter 23: (not included in free online text)
Chapter 24: Observability
Chapter 25: Minimal State-space Realization
Chapter 26: Balanced Realization
Chapter 27: Poles and Zeros of MIMO Systems
Chapter 28: Stabilization: State Feedback
Chapter 29: Observers, Model-based Controllers
Chapter 30: Minimality and Stability of Interconnected Systems

View this Free Online Material at the source:

Dynamic Systems and Control