Lecture 1 - Formulation of Dynamical Systems - I

Lecture 2 - Formulation of Dynamical Systems - II

Lecture 3 - Existence and Uniqueness Theorem - I

Lecture 4 - Existence and Uniqueness Theorem - II

Lecture 5 - Linear Systems - I

Lecture 6 - Linear Systems - II

Lecture 7 - Solutions of Linear Systems - I

Lecture 8 - Solutions of Linear Systems - II

Lecture 9 - Solutions of Linear Systems - III

Lecture 10 - Fundamental Matrix - I

Lecture 11 - Fundamental Matrix - II

Lecture 12 - Fundamental Matrix for Non-Autonomous systems

Lecture 13 - Solutions of Non-Homogeneous Systems

Lecture 14 - Stability of Systems: Equilibrium Points

Lecture 15 - Stability of Linear Autonomous Systems - I

Lecture 16 - Stability of Linear Autonomous Systems - II

Lecture 17 - Stability of Linear Autonomous Systems - III

Lecture 18 - Stability of Weakly Non-Linear Systems - I

Lecture 19 - Stability of Weakly Non-Linear Systems - II

Lecture 20 - Stability of Non-Linear Systems using Linearization

Lecture 21 - Properties of Phase Portrait

Lecture 22 - Properties of Orbits

Lecture 23 - Phase Portrait: Types of Critical Points

Lecture 24 - Phase Portrait of Linear Differential Equations - I

Lecture 25 - Phase Portrait of Linear Differential Equations - II

Lecture 26 - Phase Portrait of Linear Differential Equations - III

Lecture 27 - Poincare Bendixson Theorem

Lecture 28 - Limit Cycle

Lecture 29 - Lyapunov Stability - I

Lecture 30 - Lyapunov Stability - II

Lecture 31 - Introduction to Control Systems - I

Lecture 32 - Introduction to Control Systems - II

Lecture 33 - Controllability of Autonomous Systems

Lecture 34 - Controllability of Non-autonomous Systems

Lecture 35 - Observability - I

Lecture 36 - Observability - II

Lecture 37 - Results on Controllability and Observability

Lecture 38 - Companion Form

Lecture 39 - Feedback Control - I

Lecture 40 - Feedback Control - II

Lecture 41 - Feedback Control - III

Lecture 42 - Feedback Control - IV

Lecture 43 - State Observer

Lecture 44 - Stabilizability

Lecture 45 - Introduction to Discrete Systems - I

Lecture 46 - Introduction to Discrete Systems - II

Lecture 47 - Lyapunov Stability Theory - I

Lecture 48 - Lyapunov Stability Theory - II

Lecture 49 - Lyapunov Stability Theory - III

Lecture 50 - Optimal Control - I

Lecture 51 - Optimal Control - II

Lecture 52 - Optimal Control - III

Lecture 53 - Optimal Control - IV

Lecture 54 - Optimal Control for Discrete Systems - I

Lecture 55 - Optimal Control for Discrete Systems - II

Lecture 56 - Controllability of Discrete Systems

Lecture 57 - Observability of Discrete Systems

Lecture 58 - Stability for Discrete Systems

Lecture 59 - Relation between Continuous and Discrete Systems - I

Lecture 60 - Relation between Continuous and Discrete Systems - II