Controller synthesis for discrete‐time positive switched T–S fuzzy systems with partially controllable subsystems. Issue 4 (28th April 2021)

• Record Type: Journal Article
• Authors: Yang, Gengjiao; Hao, Fei; Zhang, Lin; Li, Bo hu
• Is Part Of: Asian journal of control. Volume 24:Issue 4(2022)
• Page Start: 1622
• Page End: 1637
• Publication Date: 2021-04-28
• Subjects: controller synthesis -- mode‐dependent average dwell time (MDADT) -- partially controllable subsystems -- positive switched systems -- T–S model; Automatic control -- Periodicals; Control theory -- Periodicals; 629.805
• DOI: 10.1002/asjc.2550
• Languages: English
• ISSNs: 1561-8625

Abstract

Abstract: The controller synthesis problem for discrete‐time positive switched T–S fuzzy systems (PSTSFSs) is investigated in this paper. Unlike previous literature, subsystems are assumed to be partially controllable in this paper. A novel slow–fast combined mode‐dependent average dwell time (SFCMDADT) approach is proposed to obtain sufficient conditions for the stability of general positive switched nonlinear systems with partially stable subsystems. Then based on the obtained results, a parallel distributed compensation (PDC)‐based fuzzy controller is designed, and sufficient conditions for the stability of PSTSFSs with partially controllable subsystems are developed with the aid of a time‐scheduled multiple linear copositive Lyapunov function. Furthermore, sufficient conditions for the stability of the positive switched T–S fuzzy system are given respectively for the two cases that the subsystems are all controllable and all uncontrollable. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed method.