Extensions of Linear Quadratic Control Theory Review of linear dynamic systems Canonical forms pole assignment and state observers Lyapunov stability theory Linear quadratic optimal control to kalman filtering The maximum principle and the Hamilton Jacobi Bellman equation The non convex case Controllability subject to controller constraints Linear quadratic problems with conical control set Special non linear quadratic formulations Hybrid criteria and parameter sensitivity Conditional definiteness of quadratic functionals Exponential performance criteria and state dependent noise Differential games Optimal control of partial differential equations.