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The Gradient Method is the most basic one among the many optimalizing methods and has been studied rather theoretically. The reports of its practical applications are scarece, because there are many difficult problems which must be solved before appling it. There has been no kinetic analysis which shows the quantitative relations among the stability, the settling time, the effects of disturbances and the system-parameters such as the sampling interval, the process time lag, the height of test signal, the proportional gain of adjustment and so on. This paper is concerned with the theoretical analysis, especially, for the stability problem. It can be shown that the time lag in the process is a dominant factor on which the system stability depends, and that the stability also depends upon the initial condition since the system has an unstable limit cycle. Finally some examples by analog simulation are given to examine the theoretical results.

Stability of the Optimalizing Control Systems by Gradient Method