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Energetistic stability of fuzzy dynamic systems

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3 Author(s)
Kiszka, Jerzy B. ; Cybernetics Research Laboratory, College of Engineering, University of Saskatchewan Saskatoon, SK S7N OWO, Canada ; Gupta, Madan M. ; Nikiforuk, Peter N.

A dynamic system is stable if its total energy decreases monotonically until a state of equilibrium is reached. The stability of a fuzzy dynamic system is based on a generalization of this notion. If a free fuzzy dynamic system has an asymptotically stable equilibrium state, the stored energy of the system displaced within the domain of attraction decays with time until it assumes its minimum value at the equilibrium state. An energy ‘measure’ of a fuzzy dynamic system is proposed and ‘an energy function’ is formulated. A heuristic algorithm for determining the stability of the fuzzy system is also proposed. To illustrate the applications of the algorithm, some numerical examples are given.

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Systems, Man and Cybernetics, IEEE Transactions on  (Volume:SMC-15 ,  Issue: 6 )