Local dynamic output feedback control of saturated discrete-time T-S fuzzy systems with partially measured premise variables

This paper aims to investigate the problem of designing locally stabilizing dynamic output feedback controllers and estimate the domain of attraction for discrete-time Takagi-Sugeno (T-S) fuzzy systems. A realistic scenario is assumed where the control signal is subject to saturation, and the premise variables are partially or completely unmeasured, that is, not available for the control law. As a result, the fuzzy output controller can have a different number of fuzzy rules and a different set of membership functions from the T-S model. To obtain locally stabilizable conditions, we propose modeling the variation rate of the membership functions without using upper bounds, a new contribution in the context of output control of discrete-time T-S systems. The design conditions are expressed as linear matrix inequality relaxations based on fuzzy Lyapunov functions using slack variables introduced by Finsler's lemma. Numerical examples illustrate the effectiveness of the approach.

Automated summary

This paper investigates the design of locally stabilizing dynamic output feedback controllers and estimates the domain of attraction for discrete-time Takagi-Sugeno (T-S) fuzzy systems. Considering the saturation effect on the control signal and the incomplete measurement of premise variables, the fuzzy output controller can have a different number of fuzzy rules and membership functions from the T-S model. To obtain local stabilizable conditions, a new approach is proposed by modeling the variation rate of membership functions without using upper bounds. The design conditions are expressed as linear matrix inequality relaxations based on fuzzy Lyapunov functions using slack variables introduced by Finsler's lemma. Numerical examples demonstrate the effectiveness of the proposed approach.