Initially introduced as a model-free control design method, in today practice fuzzy control is dominantly used as yet another nonlinear control technique based either on a linear or nonlinear model of a process. This ...
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Initially introduced as a model-free control design method, in today practice fuzzy control is dominantly used as yet another nonlinear control technique based either on a linear or nonlinear model of a process. This paper addresses the stability assessment of a fuzzy logic control system based only on the partial knowledge of a controlled process. Lyapunov stability conditions are derived and analyzed by using fuzzy numbers and fuzzy arithmetic. The experimental results obtained for a non-stable second-order system confirmed that this approach could be successfully implemented. Some questions, addressed in the paper, remained open for further investigation.
In this paper we describe a procedure that exploits geometric properties of state space in the investigation of the system stability. Although this method is cumbersome, its practical value becomes clear in the situat...
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In this paper we describe a procedure that exploits geometric properties of state space in the investigation of the system stability. Although this method is cumbersome, its practical value becomes clear in the situation when state space is reduced to a phase plane, which is the case in a second-order system. Then phase plane analysis offers well known procedures (especially in case f(.) is linear) for the determination of the system stability. Simulation results, obtained by implementation of the proposed method on the fuzzy controller design, are given at the end of the paper
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