Recurrent Takagi-Sugeno fuzzy interpolation for switched linear systems and hybrid automata

A novel perspective of fuzzy control is introduced, by combining a continuous Takagi-Sugeno (TSFS) with a discrete-time recurrent fuzzy system (RFS). The developed hybrid dynamic recurrent Takagi-Sugeno fuzzy approach enables a recurrent rule base, which leads to a dynamical interpolation law between linear subsystems. The formalism is applicable to switched systems and hybrid automaton models. The stability concerning switched systems is ensured by a common quadratic Lyapunov function. Additionally, two multiple Lyapunov function-based stability relaxation conditions are shown. For the hybrid automaton case, practical stability is analyzed. The performance of the approach is validated by simulating a car distance control system (hybrid automaton) and an experimental application to an inverted pendulum (switched control).