| The cheap control problem for a multi-input/multi-output discrete time system is initially considered, and an algorithm to find the optimal cheap control and its corresponding cost for both minimum and non minimum phase plants is presented. In contrast to the continuous time case, the limiting optimal cost associated with minimum phase discrete time plants is greater than zero. Explicit expressions for the optimal control and its associated algebraic Riccati equation for a minimum phase plant then are derived. Applications of the results obtained is then made to study the "perfect robust servomechanism problem" for a discrete system. In addition to this study, it is shown that exact asymptotic error regulation may occur in the discrete servomechanism problem for a large class of unmodelled reference/disturbance signals. |
