A New Fuzzy Lyapunov Function for Relaxed Stability Condition of Continuous-Time Takagi–Sugeno Fuzzy Systems

IEEE Transactions on Fuzzy Systems (Impact Factor: 8.75). 08/2011; 19(4):785-791. DOI: 10.1109/TFUZZ.2011.2142315
Source: DBLP


This paper presents a new fuzzy Lyapunov function (FLF) for the stability analysis of continuous-time Takagi-Sugeno (T-S) fuzzy systems. Unlike conventional FLFs, the proposed one depends not only on the fuzzy weighting functions of the T-S fuzzy systems but on their first-order time derivatives as well. Based on the proposed FLF, a sufficient stability condition is derived in the form of linear matrix inequalities, depending on the upper bounds on the second-order time derivative of the fuzzy weighting functions, as well as the first-order ones. Finally, some examples demonstrate that the proposed condition can provide less conservative results than the previous ones in the literature.

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Available from: Young Hoon Joo, Jan 25, 2014
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    • "In general, a common quadratic Lyapunov function approach was used to deal with stability and stabilization issues for type-1 T–S fuzzy systems. Several nonquadratic Lyapunov functions were also proposed to derive less conservative results [6] [7] [8] [9] [10] [11] [12] [13] [14]. On the other hand, most existing results were obtained by parallel distributed compensation (PDC) scheme. "
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    • "Moreover, the fuzzy control can integrate with other control techniques; for example, [17] applies the fuzzy logic system to the sliding mode control and [18] [19] integrate the fuzzy control with the proportional integral derivative (PID) technique. Lyapunov theory is a common approach being used to analyze the stability of fuzzy controller [20] [21]. Some literatures try to obtain the optimal controller parameters and analyze the fuzzy controller's performance. "
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    • "It is well known that the Takagi-Sugeno (T-S) linear systems can be used to approximate smooth complex systems. Therefore , recently, fuzzy systems based on Takagi-Sugeno (T-S) [1] [2] [3] [4] [5] [6] [7] [8] model have attracted a lot of attention [9] [10] [11] [12] [13] [14] [15] [16]. In [17], the parameterized linear matrix inequality techniques were used in fuzzy control system design. "
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