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Control Systems
Course Description
This course covers fundamentals of linear dynamical systems and
control at a graduate level for students in electrical or mechanical
engineering. Topics include state-space analysis of continuous and discrete
multivariable systems, controllability and observability, sensitivity considerations, stability of
linear and nonlinear systems.
Course Outline and Syllabus
Course syllabus.
- Introduction: Examples, notation, first-order differential equations. State-space vs.
input-output descriptions.
- Closed-form solutions: State-transition matrix in continuous-time and discrete-time sys-
tems. Modes, asymptotic behavior. Qualitative response.
- Stability: Equilibrium points, Lyapunov stability, Lyapunov equation. Linearization. Input-
output stability.
- Controllability and observability: Reachability, duality, Grammians.
- Uncontrollable / unobservable systems: Stabilizability, detectability. Decomposition
theorem.
- Internal / external descriptions: Relationship between state-space and input-output
descriptions. Lyapunov and input-output stability.
- Realization theory: Minimal realizations, realization algorithms.
- State feedback and state observers: LQR. Full-order and reduced-order observers. State
estimation, LQG.
- Feedback: Interconnected systems, parameterized controllers.
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