Modern control is based on the concept of a state for modeling dynamical systems. This course considers both continuous-time and discrete-time systems, focusing primarily on the case of a digital controller. The course starts with the study of deterministic systems, covering observability, controllability, stability, and state-variable feedback. Consideration of stochastic disturbances leads to Kalman filter algorithms for state estimation and system identification. Students will develop computer simulations involving classical Kalman filters, numerically superior square-root algorithms, and extended and unscented Kalman filters for systems that are nonlinear or have non-Gaussian or non-additive disturbances. The concept of state is then extended to control based on reinforcement learning. The course also provides an introduction to optimal control. Prerequisites: Undergraduate courses in linear algebra and either multivariate calculus or signals and systems.