Abstract: Abstract： In this paper, the realization methods of “sum of all coefficients being one (SACO)” for the strongly uncertain system are researched, where the strongly uncertain system means that its static gain and its bound are unknown and the range of the static gain is large. The principle SACO was found by Prof. Hongxin Wu in 1980’, which shows that the sum of the coefficients for the discretized systems of unknown continuous systems is one under certain conditions, playing an important role on the solution to the key problems in closeloop identification and adaptive control. A transformation is needed for systems to realize the conditions because the SACO holds under certain conditions, where using the reciprocal of the nominal value of the static gain as the input transformation has been widespread utilized due to easy implementation. However, when the uncertainties are larger, the transformation will bring larger errors. This problem is deeply investigated in this paper. We specifically show that the effects on the realization of SACO of the ratio between the uncertainties and the nominal value of the static gain. When the ratio is lower, the SACO can be realized approximately; otherwise, when the ratio is higher, we need to furthermore choose appropriate sampling duration to approximately realize the SACO. The conclusions obtained in this paper lay certain foundation on the practical applications of the characteristic model theory.

Key words: Keywords： Sum of all coefficients equals to one (SACO), strongly uncertain systems, realization method, static gain, input transformation