Admissibility Analysis and Control Synthesis for T-S Fuzzy Descriptor Systems

• Published in: IEEE transactions on fuzzy systems Vol. 25; no. 4; pp. 729 - 740
• Main Authors: Qiao, Liang, Zhang, Qingling, Zhang, Guofeng
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.08.2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Admissible control; Compensation; Controllers; Design methodology; Fuzzy systems; Linear matrix inequalities; linear matrix inequalities (LMIs); Lyapunov methods; Mathematical analysis; Mathematical models; Matrix methods; nonparallel distributed compensation (non-PDC) controller; nonquadratic fuzzy Lyapunov function; parallel distributed compensation (PDC) controller; PD control; Stability analysis; Symmetric matrices; Synthesis; Takagi–Sugeno (T–S) fuzzy descriptor system
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2016.2574917

The problem of admissibility analysis and control synthesis for Takagi-Sugeno fuzzy descriptor systems is investigated. First, based on Nonquadratic fuzzy Lyapunov function and fully using the information of fuzzy membership functions, a new relaxed sufficient condition ensuring a fuzzy descriptor system to be admissible (regular, impulse-free, and stable) is proposed, in which it is not necessary to require every fuzzy subsystem to be stable. Second, the other sufficient condition for the admissibility is obtained without the information of time derivatives of fuzzy membership functions. Following the analysis, both parallel and nonparallel distributed compensation controllers are designed, linear matrix inequalities conditions are given to construct the controllers. Finally, some examples are provided to illustrate the main results in this paper less conservative than some earlier related results.