Output feedback control of discrete-time nonlinear systems with unknown time-delay based on Takagi-Sugeno fuzzy models

In this paper, a new discrete-time fuzzy output feedback control method for nonlinear systems with unknown time-delay is proposed. The method follows on from the analysis and design method for a fuzzy controller and observer proposed by Ma et al. (IEEE T Fuzzy Syst (1998) 6(1):41–51), and the extension of this to nonlinear systems with known time-delay by Cao et al. (IEEE T Fuzzy Syst (2000) 8(2):200–211) For the case of unknown time-delay, we derive the sufficient condition for the asymptotic stability of the equilibrium point by applying Lyapunov-Krasovskii theorem and convert this condition into the famous LMI problem.