Fuzzy-rule-based model reduction for switched nonlinear systems

• Published in: Chinese Control Conference pp. 3716 - 3720
• Main Authors: Su, Xiaojie, Xia, Fengqin, Liu, Xinxin, Yang, Rongni
• Format: Conference Proceeding Journal Article
• Language: English
• Published: TCCT 01.07.2016
• Subjects: Algorithms; Approximation; Constraint modelling; Control theory; Dynamical systems; Fuzzy; hybrid systems; Mathematical analysis; model approximation; Model reduction; Nonlinear dynamics; Nonlinear systems; Nonlinearity; Reduced order systems; Stability; Switched systems; Switches; System performance
• ISSN: 1934-1768
• DOI: 10.1109/ChiCC.2016.7553932

The reduced-order model approximation problem is investigated for discrete-time nonlinear switched systems in T-S fuzzy framework in this paper. For a high-dimensional hybrid nonlinear system, our aim is focused on the construction of a reduced-dimensional hybrid model, which not only approximates the original system well with a pre-specified system performance level but also translates it into a lower-dimensional multi-mode system. Based on the average dwell time technique and the piecewise Lyapunov function technique, a sufficient condition is first proposed to guarantee the mean-square exponential stability with a weighted ℋ ∞ system performance level for the augmented error system. The model approximation problem with pre-specified performance is solved by using the projection technique, which casts the reduced-order hybrid model into a sequential minimization problem subject to linear matrix inequality constraints by employing the cone complementary linearization algorithm.