Syllabus

Fundamentals of matrix algebra and vector spaces – Solution of simultaneous equations for square, under-determined, and over-determined systems – Concepts of basis vector transformations – Sim- ilarity and adjoint transformations – Eigenvalues and eigenvectors – Jordan form – Characteristic equation – Analytic functions of square matrices and Cayley-Hamilton theorem – Concepts of state, state-space, state-vector – Methods for obtaining the system mathematical model in the state-space form – State-space Form for Aerospace Systems: Aircraft dynamics, missile dynamics, inertial navi- gation system – Solution of homogeneous state equations – Concept of fundamental matrix and state transition matrix – Methods for evaluating state transition matrix – Solution of nonhomogeneous equations – Phase variable and Jordan canonical forms – Controllability and observability of the systems, pole placement design with full state feedback – Introduction to optimal control.