Abstract
Generally, the continuous and discrete TS fuzzy systems’ control is studied independently. Unlike the discrete systems, stability results for the continuous systems suffer from conservatism because it is still quite difficult to apply non-quadratic Lyapunov functions, something which is much easier for the discrete systems. In this paper and in order to obtain new results for the continuous case, we proposed to connect the continuous with the discrete cases and then check the stability of the continuous TS fuzzy systems by means of the discrete design approach. To this end, a novel frame was proposed using the sum of square approach (SOS) to check the stability of the continuous Takagi Sugeno (TS) fuzzy models based on the discrete controller. Indeed, the control of the continuous TS fuzzy models is ensured by the discrete gains obtained from the Euler discrete form and based on the non-quadratic Lyapunov function. The simulation examples applied for various models, by modifying the order of the Euler discrete fuzzy system, are presented to show the effectiveness of the proposed methodology.
Highlights
The stability results in the continuous case suffer from conservatism since it is still quite difficult to use the non-quadratic Lyapunov functions, while it is much easier in the discrete case
To overcome such a problem, a novel method of stability analysis for the continuous systems was proposed using the controller obtained from the Euler discretized model
The sum of square approach (SOS) approach was adopted to check the stability of continuous systems with discrete gains
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Since their introduction in 1985, Takagi Sugeno fuzzy models have been studied for the control of a wide class of nonlinear systems owing to their ability to deal with complex behaviors [1]. In this case, the nonlinear systems can be represented by a set of linear subsystems linked to nonlinear functions.
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