 Lecture 1: Examples of control systems
 Lecture 2: Linear control systems and linearization of nonlinear control systems
 Lecture 3: Singleinput 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 complexvalued 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:
Frequency response and bode plots
 Lecture 21:
Notions of stability for control systems
 Lecture 22:
Internal stability and asymptotic stability for linear control systems
 Lecture 23:
Lyapunov stability for nonlinear dynamical systems I
 Lecture 24:
Lyapunov stability for nonlinear dynamical systems II
 Lecture 25:
Lyapunov equations for linear systems
 Lecture 26:
Control Architectures: Openloop and closedloop control
 Lecture 26♠:
Rouche's theorem and continuous dependency of roots of polynomials on their coefficients
 Lecture 27:
Why closedloop control? Reference tracking along with disturbance rejection
 Lecture 28:
Reference tracking and disturbance rejection for a DCmotor: Poleplacement for controllable LTI systems
 Lecture 29:
Limitations of proportional feedbacks: PD and PID controllers, causality and delay, and windup 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:
Gain and phase crossovers and margins of stability I
 Lecture 34:
Small gain theorem
 Lecture 35:
Small gain theorem vs. Nyquist theorem
 Lecture 36:
Review session
