This paper proposes a new method to design the observer for state delay systems such that (i) state estimation errors converge to zero quickly and (ii), at the same time, a quadratic performance measurement of the deviation of estimates from the actual states is minimized for reducing large error during the transient period of observation. The proposed new approach fuses the merits of both the orthogonal functions approach and evolutionary optimization. One illustrative example is given to verify the effectiveness and efficiency of the proposed new optimization method on performance improvement of state estimations. From the illustrative example, in addition to the asymptotical convergence of the estimated state errors, the performance index for the proposed optimal design approach is clearly much lower than that of the nonoptimal design method.
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