On the Foundations of Fuzzy Dynamical System Theory: Controllability and Observability

The controllability and the observability of fuzzy dynamical system are studied. The uncertainty of the fuzzy dynamical system is due to the initial condition. The available information on the uncertainty can be described via a membership function. In this paper, we propose a systematic approach to investigate the controllability and the observability of fuzzy dynamical system via the use of the membership function. The concepts of the controllability and the observability in the fuzzy sense are presented via the use of the membership function. The necessary and sufficient conditions for the controllability and the observability of the linear time-variant and time-invariant uncertain system are derived. As a result, the paper lays the foundation for the control of fuzzy dynamical system.

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