- Lecture 1: Examples of control systems
- Lecture 2: Linear control systems and linearization of nonlinear control systems
- Lecture 3: Single-input single output linear control systems
- Lecture 4: Uniqueness of solutions for LTI control systems
- Lecture 5: Existence of analytic solutions to linear matrix differential equation
- Lecture 6: Properties of matrix exponentials
- Lecture 7: Solutions of SISO linear control systems
- Lecture 8: Kalman's criterion of controllability of LTI systems I
- Lecture 9: Kalman's criterion of controllability of LTI systems II
- Lecture 10: Observability for LTI system
- Lecture 11: Laplace transforms and their abscissa of convergence
- Lecture 12: Properties of Laplace transforms
- Lecture 13: Transfer functions for LTI systems
- Lecture 14:
Space of smooth functions with bounded support, distributions, and impulse response to point distributions
- Lecture 15: Properties of transfer functions related to controllability and observability
- Lecture 16:
Realization theory: Real rational complex-valued proper functions and transfer functions
- Lecture 17:
Canonical controllable and observable realizations
- Lecture 18:
The relationship between frequency response, impulse response, and transfer functions
- Lecture 19:
Frequency response and bode plots
- Lecture 20:
Notions of stability for control systems
- Lecture 21:
Internal stability and asymptotic stability for linear control systems
- Lecture 22:
Lyapunov stability for nonlinear dynamical systems
- Lecture 23:
Lyapunov equations for linear systems
- Lecture 24:
Observability and controllability energy I
- Lecture 25:
Observability and controllability energy II
- Lecture 26:
Control Architectures: Open-loop and closed-loop control
- Lecture 26♠:
Rouche's theorem and continuous dependency of roots of polynomials on their coefficients
- Lecture 27:
Why closed-loop control? Reference tracking along with disturbance rejection
- Lecture 28:
Reference tracking and disturbance rejection for a DC-motor: Pole-placement for controllable LTI systems
- Lecture 29:
Limitations of proportional feedbacks: PD and PID controllers, causality and delay, and wind-up phenomenon
- Lecture 30:
The Principle of Arguments and the Nyquist Theorem I
- Lecture 31:
The Principle of Arguments and the Nyquist Theorem II
- Lecture 32:
The Principle of Arguments and the Nyquist Theorem III
- Lecture 33:
System gain
- Lecture 34:
Small gain theorem
- Lecture 35:
Small gain theorem vs. Nyquist theorem
- Lecture 36:
Review session
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