Abstract
This paper focuses on the guaranteed cost stability analysis of fuzzy-model-based (FMB) control systems. Representing the nonlinear plant using a Takagi–Sugeno (T–S) fuzzy model, a fuzzy controller is employed to close the feedback loop. A weighted linear quadratic cost function is considered as the cost index to measure the performance of the closed-loop fuzzy system in terms of the system states, system outputs, and control signals. The stability of the FMB control system is investigated by the Lyapunov stability theory subject to the minimization of cost index for performance realization. A membership-function-dependent approach using the piecewise-linear membership functions is employed to include the information of membership functions into the stability analysis. Membership-function-dependent stability conditions in terms of linear matrix inequalities are obtained to determine the system stability and feedback gains with the consideration of the system performance measured by the cost function. A simulation example is provided to illustrate the effectiveness and merits of the proposed approach.
Highlights
Takagi–Sugeno (T–S) fuzzy model was first developed by Takagi and Sugeno in 1985 [1], which provided an effective model to represent nonlinear plants which facilitates the system analysis and control synthesis
This paper focuses on the guaranteed cost stability analysis of fuzzy-model-based (FMB) control systems
Given that only the specific membership functions used in Takagi– Sugeno (T–S) fuzzy model and fuzzy controller are needed to be considered in the control problem, the stability conditions are relatively conservative if the FMB control systems are unnecessarily guaranteed stable under all kinds of membership functions
Summary
Takagi–Sugeno (T–S) fuzzy model was first developed by Takagi and Sugeno in 1985 [1], which provided an effective model to represent nonlinear plants which facilitates the system analysis and control synthesis. The work in [10] used the symmetry property of the membership functions of the T–S fuzzy model and fuzzy controller in the analysis and managed to relax the LMI-based stability conditions. If the premise rules of the fuzzy controller are different from those of the T–S fuzzy model, the stability analysis results will be very conservative as the permutations of the membership functions used in the PDC design cannot be applied due to the mismatched premised membership functions. Given that only the specific membership functions used in T–S fuzzy model and fuzzy controller are needed to be considered in the control problem, the stability conditions are relatively conservative if the FMB control systems are unnecessarily guaranteed stable under all kinds of membership functions.
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