ECSE 501. Linear Systems.

Mathematical models of linear systems, fundamental solution and transition matrices, non-homogeneous linear equations, controllability and observability of linear systems, reachable subspaces, Cayley-Hamilton's Theorem, Kalman's controllability and observability rank conditions, minimal realizations, frequency response, invariant subspaces, finite and infinite horizon linear regulator problems, uniform, exponential, and input-output stability, the Lyapunov equation.