Week 1 : Formulation of physical systems-I, Formulation of physical systems-II, Existence and uniqueness theorems-I, Existence and uniqueness theorems-II, Linear systems-I
Week 2 : Linear Systems-II, Solution of linear systems-I, Solution of linear systems–II, Solution of linear systems-III, Fundamental Matrix-I
Week 3 : Fundamental Matrix-II, Fundamental matrices for non- autonomous systems, Solution of non-homogeneous systems , Stability of systems: Equilibrium points, Stability of linear autonomous systems-I
Week 4 : Stability of linear autonomous systems-II, Stability of linear autonomous systems-III, Stability of weakly non- linear systems-I, Stability of weakly non- linear systems-II, Stability of non- linear systems using linearization
Week 5 : Properties of phase portrait, Properties of orbits, Phase portrait : Types of critical points, Phase portrait of linear differential equations-I, Phase portrait of linear differential equations-II
Week 6 : Phase portrait of linear differential equations-III, Poincare Bendixson Theorem, Limit cycle , Lyapunov stability-I, Lyapunov stability–II
Week 7 : Introduction to Control Systems-I, Introduction to Control Systems-II, Controllability of Autonomous Systems, Controllability of Non-autonomous Systems, Observability-I
Week 8 : Observability-II, Results on Controllability and Observability, Companion Form, Feedback Control-I, Feedback Control-II
Week 9 : Feedback Control-III, Feedback Control-IV, State Observer, Stabilizability, Introduction to Discrete Systems-I
Week 10 : Introduction to Discrete Systems-II, Lyapunov Stability Theory-I, Lyapunov Stability Theory-II, Lyapunov Stability Theory-III, Optimal Control- I
Week 11 : Optimal Control-II, Optimal Control-III, Optimal Control- IV, Optimal Control for Discrete Systems-I, Optimal Control for Discrete Systems-II
Week 12 : Controllability of Discrete Systems, Observability of Discrete Systems, Stability for Discrete Systems, Relation between Continuous and Discrete Systems-I, Relation between Continuous and Discrete Systems-II
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