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Stability analysis of polynomial fuzzy-model-based control systems under perfect/imperfect premise matching

Stability analysis of polynomial fuzzy-model-based control systems under perfect/imperfect premise matching

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This study presents an improved sum-of-squares (SOS)-based stability analysis result for the polynomial fuzzy-model-based control system, formed by a polynomial fuzzy model and a polynomial fuzzy controller connected in a closed loop. Two cases, namely perfect and imperfect premise matching, are considered. Under the perfect premise matching, the polynomial fuzzy model and polynomial fuzzy controller share the same premise membership functions. While different sets of membership functions are employed, it falls into the case of imperfect premise matching. Based on the Lyapunov stability theory, improved SOS-based stability conditions are derived to determine the system stability and facilitate the controller synthesis. Simulation examples are given to verify the stability analysis results and demonstrate the effectiveness of the proposed approach.

Inspec keywords: closed loop systems; polynomials; fuzzy set theory; Lyapunov methods; stability; fuzzy control

Other keywords: closed loop system; polynomial fuzzy-model-based control system; SOS-based stability condition; imperfect premise matching; Lyapunov stability theory; sum-of-squares-based stability analysis; membership function

Subjects: Combinatorial mathematics; Algebra; Stability in control theory; Fuzzy control

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