Observer synthesis for uncertain Takagi–Sugeno fuzzy systems with multiple output matrices

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Abstract
Designing an observer for Takagi–Sugeno (T–S) fuzzy systems in the presence of uncertainties is a great challenge for researchers. Owing to the uncertainties, it is hard to design an observer to make the state estimation error converge to zero asymptotically. To resolve this problem, the authors consider the uncertainties to be unknown inputs and apply the unknown inputs method. The existing literature concerning observer design for T–S fuzzy systems using the unknown inputs method generally have only a single output matrix. In addition, the method of converting uncertainties into unknown inputs requires a matching condition which includes a common constant matrix to match all uncertainties in all local models of T–S fuzzy system. Therefore, the above two constraints lead the observer design to be very conservative. To overcome the above drawbacks, a special transformation is used to transform the original T–S fuzzy system into a new system form, and then they propose a method to synthesise an observer for an uncertain T–S fuzzy system which allows different output matrices and relaxes the matching condition of the uncertainties for all local models. Finally, two examples are presented to demonstrate the efficiency of the proposed method.

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