Stability Analysis of Fuzzy Model-based Control Systems with Knowledge on Membership Functions' Shapes

Download or read book Stability Analysis of Fuzzy Model-based Control Systems with Knowledge on Membership Functions' Shapes written by Mohammad Narimani and published by . This book was released on 2011 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis using fuzzy logic methodology, the stability of complex nonlinear control systems is investigated. Fuzzy-Model-Based (FMB) control system offers a systematic platform in handling control problems from the point of view of stability analysis. In this platform, Membership Functions (MFs) gather the overall nonlinear properties of the control system. The lack of the information of MFs is one the main sources of conservativeness in the current stability analysis approaches. To widen the applicability of the FMB control scheme, the aim of the proposed research the¬sis is to derive less conservative stability conditions. Therefore, some attempts are made to obtain relaxed shape-dependent stability conditions. The results of this investigation are presented in three parts as follows: 1. The stability analysis of FMB control systems under Parallel Distributed Com¬ pensation (PDC) is carried out. First, the stability conditions, which are the inequal¬ ities in the form of p-dimensional fuzzy summation, are expanded to n-dimensional fuzzy summation (n > p). The global and regional boundary information of MFs are then utilized for relaxation of stability analysis results and two analysis approaches are proposed namely Global-Membership-Function-Shape-Dependent (GMFSD) ap¬ proach and Regional-Membership-Function-Shape-Dependent (RMFSD) approach, respectively. For RMFSD approach the operating region is partitioned into subre- glons and the boundary information of MFs on all operating subregions are employed to facilitate the stability analysis. The stability conditions are derived in the form of Linear Matrix Inequality (LMI). 2. Employing Sum of Squares (SOS) approach, relaxed stability conditions for Polynomial-Fuzzy-Model-Based (PFMB) control systems are derived. First, MFs are approximated by some polynomials in the partitioned operating domain of MFs.