Time-delayed feedback control of chaotic T-S fuzzy systems

This paper deals with the time-delayed feedback control of periodic orbits in the chaotic T-S fuzzy systems. A chaotic system has embedded within it an infinite number of unstable periodic orbits (UPO´s). Tracking UPO´s is of particular interest in chaos-control research. A novel and efficient idea is to control by means of time-delayed feedback control (TDFC). Recently, a number of analytic T-S fuzzy systems for the chaotic systems have been found. Thus it is interesting to design a controller under the framework of TDFC. A analytic sufficient condition for the chaotic T-S fuzzy systems from the TDFC approach is derived in terms of linear matrix inequalities (LMIs). A gradient-decent based adaptation algorithm is incorporated with the fuzzy-model-based TDFC to estimate the period of the UPO. The established theoretical results are clarified by the numerical example.