### A Lyapunov Function for Vector Control Drives in Induction Machines

#### Abstract

In this paper a useful Lyapunov function for vector control of induction machines is introduced. To do this, some beneficial theorems are reviewed and by applying these theorems and state equations to a vector control drive, its candidate Lyapunov function is achieved. Range of set points such as reference speed, reference flux linkage values and speed controller gain is obtained for such a drive and therefore these values can be set offline to avoid unstable behavior. The simulated and experimental results are given in the last section of the paper to show the efficacy of the given Lyapunov function.

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