Dead-beat control and the Riccati equation

Connections between dead-beat control strategies and optimal control policies for linear, time-invariant, discrete-time systems are established. The performance index of the system is quadratic and only the terminal state of the system is penalized. An explicit solution to the singular Riccati equation, associated with this optimization problem, is given. Properties of the time-variable gain matrices, generating the optimal cantrol policy, are presented. In particular, necessary and sufficient conditions for each of these gain matrices to be a time-invariant deadbeat controller are given.