Introduction, Fields, Vectors and Vector Spaces, Linear Combinations and Bases, Linear Transformations and Matrices, Scalar Product and Norms, Solution of Linear Algebraic Equations, Eigen values, Eigen vectors and a Canonical-Form, Functions of a Square Matrix.
Introduction, The Concept of State, State Equations for Dynamic Systems, Time-Invariance and Linearity, Non uniqueness and State Model, State diagrams.
Introduction, Linear Continuous-Time Models, Linear Discrete-Time Models, Nonlinear Models, Local Linearization of Nonlinear Models, Plant Models of some Illustrative Control Systems.
Introduction, Existence and Uniqueness of Solutions to Continuous –Time State Equations, Solution of Nonlinear Continuous-Time Equations, Solution of Linear Time-Varying Continuous –Time State Equations, Solution of Linear Time- Invariant continuous-Time State Equations, Solution of Linear Discrete-Time State Equations, State Equations of Sampled –Data Systems.
Introduction, General Concept of Controllability, General Concept of Observability, Controllability Tests for Continuous-Time Systems, Observability Tests for Continuous- Time Systems, Controllability and Observability of Discrete-Time Systems, Controllability and Observability of State Model in Jordan Canonical Form, Loss of Controllability and Observability due to Sampling, Controllability and Observability, Canonical Forms of State Model.
Introduction, Input-output Maps from State Models, Output Controllability, Reducibility, State models from Input-Output Maps.
Introduction, Stability Concepts and Definitions, Stability of Linear Time-Invariant Systems, Equilibrium Stability of Nonlinear Continuous-Time Autonomous Systems, The Direct Method of Lyapunov and the Linear Continuous-Time Autonomous Systems, Aids to Finding Lyapunov Functions for Nonlinear Continuous-Time Autonomous Systems, Use of Lyapunov Functions to Estimate Transients, The Direct Method of Lyapunov and the Discrete-Time Autonomous Systems.
Introduction, Controllable and Observable Companion Forms, The effect of State Feedback on Controllability and Observability, Pole Placement by State Feedback, Full-Order Observers, Reduced-Order Observers, Deadbeat Control by State Feedback, Deadbeat Observers