Sampled-data fuzzy controller for time-delay nonlinear systems : fuzzy-model-based LMI approach

Abstract

This paper presents the stability analysis and performance design for a sampled-data fuzzy control system with time delay, which is formed by a nonlinear plant with time delay and a sampled-data fuzzy controller connected in a closed loop. As the sampled-data fuzzy controller can be implemented by a microcontroller or a digital computer, the implementation time and cost can be reduced. However, the sampling activity and time delay, which are potential causes of system instability, will complicate the system dynamics and make the stability analysis much more difficult than that for a pure continuous-time fuzzy control system. In this paper, a sampled-data fuzzy controller with enhanced nonlinearity compensation ability is proposed. Based on the fuzzy-model-based control approach, linear matrix inequality (LMI)-based stability conditions are derived to guarantee the system stability. By using a descriptor representation, the complexity of the sampled-data fuzzy control system with time delay can be reduced to ease the stability analysis, which effectively leads to a smaller number of LMI-stability conditions. Information of the membership functions of both the fuzzy plant model and fuzzy controller are considered, which allows arbitrary matrices to be introduced, to ease the satisfaction of the stability conditions. An application example will be given to show the merits and design procedure of the proposed approach. Furthermore, LMI-based performance conditions are derived to aid the design of a well-performed sampled-data fuzzy controller.