Stability Analysis of a Type of Takagi-Sugeno PI Fuzzy Control Systems Using Circle Criterion

Abstract

A type of Takagi-Sugeno (T-S) Proportional-Integral (PI) fuzzy controllers is studied. The T-S PI fuzzy controller is formed by a T-S Proportional-Derivative (PD) fuzzy controller connected with an integrator. In this particular structure, the T-S PD fuzzy controller is a weighted sum of some linear PD sub-controllers. The mathematical properties of our T-S PI fuzzy controller are also investigated. Based on these properties, the global asymptotic stability of the fuzzy control systems, in which the T-S PI fuzzy controllers are employed, are analyzed by using the well-known circle criterion. A sufficient condition with an elegant graphical interpretation in the frequency domain is further derived to guarantee the global asymptotic stability of the above fuzzy control systems. Finally, two numerical examples are provided to demonstrate how to deploy this method in analyzing the T-S PI fuzzy control systems in the frequency domain with the aid of some simple graphs.

A note on the rates of uniform approximation of fuzzy systems

“…Moreover, suppose that χ has finite αth absolute moment (0 < α 2). Then for all f ∈ Lip * (C(U ), α), there exists a fuzzy system F k defined by (3)…”

“…Linguistic fuzzy IF -THEN rules can be developed by human experts who are familiar with the process under consideration. Fuzzy systems have been developed to solve many different practical problems such as pattern recognition 1 , system identification 2 , adaptive control 3,4,5,6 , etc. Fuzzy systems offer a key advantage over traditional approaches, expecially in fuzzy control systems.…”

fuzzy PID control synthesis for Takagi–Sugeno fuzzy systems

“…For the T–S fuzzy PID control systems, the analytical structure analysis is explored in [16, 17], where the results show that a T–S fuzzy PID controller is a non‐linear PID controller with variable gains. The stability analysis of T–S fuzzy PID control systems is investigated based on the small gain theorem [17], the passivity theory [18], the describing function method [19], and the circle criterion [20, 21]. The T–S fuzzy PID controllers are applied to human arterial pressure control [16] and motor control [22].…”