Control theory
Graduate · Engineering
Syllabus focus
Theoretical / proof-based
Pricing
Graduate-level rates are set on consultation. See the pricing page for K–12 and undergraduate rates.
Topics typically covered
Theoretical / proof-based
State-space analysis and stability
- Linear state-space models: controllability canonical forms
- Controllability and observability Grammians
- Kalman decomposition and minimal realizations
- Lyapunov stability definitions and theorems
- Lyapunov equation for linear systems
- LaSalle's invariance principle
- Input-to-state stability (ISS) concepts
- Feedback linearization conditions
- Zero dynamics and relative degree
- Stabilization of nonlinear systems via Lyapunov design
Optimal and robust control
- Calculus of variations and Pontryagin's maximum principle
- Linear quadratic regulator (LQR) derivation
- Algebraic Riccati equation properties
- Linear quadratic Gaussian (LQG) separation principle
- H-infinity control problem formulation
- Small-gain theorem and robust stability
- Structured uncertainty and μ-analysis intro
- Model reduction for large-scale plants
- Dissipativity theory and passivity
- Semidefinite programming in control (survey)
Notes
Topics reflect graduate control theory courses for engineering students emphasizing proofs and state-space methods. Prior coursework in linear algebra and signals & systems is assumed.