Linear Riccati Dynamics, Constant Feedback, and Controllability in Linear Quadratic Control Problems

Conditions are derived for linear-quadratic control (LQC) problems to exhibit linear evolution of the Riccati matrix and constancy of the control feedback matrix. One of these conditions involves a matrix upon whose rank a necessary condition and a sufficient condition for controllability are based. Linearity of Riccati evolution allows for rapid iterative calculation, and constancy of the control feedback matrix allows for time-invariant comparative static analysis of policy reactions.