Performance of suboptimal linear control systems

It is shown that the calculation of the performance of a class of suboptimal linear control systems is similar to the calculation of the performance of an equivalent optimal system. The performances of both optimal and suboptimal linear systems have terms for cost owing to uncertainty about the initial state of the plant, a nonzero mean of the initial state, error in the estimate of the state, and error in control owing to additive noise at the input. A suboptimal system, in addition to having greater costs than the optimal system for each of these terms, has a cost term which vanishes if either optimal control or optimal estimation is used.