# A New Design Method for T-S Fuzzy Controller with Pole Placement Constraints

• Joh, Joongseon (Department of control and Instrumentation Engineering Changwon National University) ;
• Jeung, Eun-Tae (Department of control and Instrumentation Engineering Changwon National University) ;
• Chung, Won-Jee (Department of Mechanical Design and Manufacturing Changwon National University) ;
• Kwon, Sung-Ha (Department of control and Instrumentation Engineering Changwon National University)
• Published : 1997.08.01

#### Abstract

A new design method for Takagi-Sugeno (T-S in short) fuzzy controller which guarantees global asymptotic stability and satisfies a desired performance is proposed in this paper. The method uses LMI(Linear Matrix Inequality) approach to find the common symmetric positive definite matrix P and feedback fains K/sub i/, i= 1, 2,..., r, numerically. The LMIs for stability criterion which treats P and K'/sub i/s as matrix variables is derived from Wang et al.'s stability criterion. Wang et al.'s stability criterion is nonlinear MIs since P and K'/sub i/s are coupled together. The desired performance is represented as $LMIs which place the closed-loop poles of$ local subsystems within the desired region in s-plane. By solving the stability LMIs and pole placement constraint LMIs simultaneously, the feedback gains K'/sub i/s which gurarntee global asymptotic stability and satisfy the desired performance are determined. The design method is verified by designing a T-S fuzzy controller for an inverted pendulum with a cart using the proposed method.

#### References

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