This paper presents the stability analysis of polynomialfuzzy-model-based (PFMB) controlsystem, formed by a polynomialfuzzymodel and a fuzzycontroller connected in a closed loop, using sum-of-squares (SOS) approa...
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(纸本)9781424469208
This paper presents the stability analysis of polynomialfuzzy-model-based (PFMB) controlsystem, formed by a polynomialfuzzymodel and a fuzzycontroller connected in a closed loop, using sum-of-squares (SOS) approach. Unlike the published work, the PFMB controlsystem is not required that the polynomialfuzzycontroller shares the same premises membership functions as those of the polynomialfuzzymodel. Piecewise linear membership functions are employed to approximate the membership functions of the polynomialfuzzymodel and polynomialfuzzycontroller to facilitate stability analysis and controller synthesis with consideration of approximation error. The piecewise linear membership functions offer a nice property that the grades of membership are governed by a finite number of sampled points. It is worth mentioning that the piecewise linear membership functions, which are not necessarily implemented physically, are a tool to carry out the stability analysis. The nice property of the piecewise linear membership functions allows them to be brought to the SOS-based stability conditions derived based on the Lyapunov stability theory. Consequently, the proposed SOS-based stability conditions are applied to PFMB controlsystems with the specified piecewise linear membership functions rather than any shapes. A simulation example is given to verify the stability analysis results and demonstrate the effectiveness of the proposed approach.
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