An alternative stability proof for “Adaptive type-2 fuzzy estimation of uncertainties in the control of electrically flexible-joint robots”

Abstract

This short note points out an improvement on the robust stability analysis for electrically driven flexible joint robots (EDFJR) given in the 2017 paper by Zirkohi and Fateh, entitled “Adaptive type-2 fuzzy estimation of uncertainties in the control of electrically flexible-joint robots.” In their paper, the authors present an interval Type-2 Adaptive fuzzy control scheme for EDFJR. The nonlinearities associated with actuator input constraints have been also considered in their paper. They discussed the saturated and unsaturated region of the control input separately and neglected the transition state between these regions. Moreover, they did not guarantee the stability of the closed-loop system in the saturated area. In this note, an alternative stability proof is presented that does not require this separation, and which guarantees the stability in a more general framework. The overall closed-loop system is proven to be robust, and bounded-input, bounded-output stable, while the motor/joint position errors are uniformly-ultimately bounded based on the Lyapunov's stability concept.