Cost sensitivity analysis for discrete-time optimal feedback controllers with time-multiplied performance indexes

The sensitivity of a class of N-th order time-multiplied performance costs for discrete-time optimal output feedback systems is investigated. Sensitivity matrices for optimal costs are evaluated with respect to variations in system parameters and design variables. The derivation of sensitivity matrices can be readily obtained by considering the Lagrangian of the performance index. It is shown that while faster system response performance can be obtained by designing with higher order time-multiplying factor in the performance index, the design also increases the optimum cost of control and absolute cost sensitivity, as can be expected.