Linear Dynamical Systems

State-space representation of linear dynamical systems. Eigenvalues of non-symmetric matrices. Left and right eigenvectors, with dynamical interpretation. Matrix exponential, stability, and asymptotic behavior. Multi-input/multi-output systems, impulse and step matrices. Convolution and transfer-matrix descriptions. Control, reachability, and state transfer. Observability and least-squares state estimation. Positive systems and Perron-Frobenius theory. Response of linear dynamical systems to Gaussian random inputs. The linear-quadratic regulator and the Kalman filter. Applications from a broad range of disciplines including circuits, signal processing, machine learning, and control systems.