Specific stability region analysis for uncertain fuzzy descriptor systems with multiple derivative matrices

Abstract

This paper addresses the specific stability region for uncertain fuzzy descriptor systems with distinct derivative matrices in the rules. First, an equivalent poles’ location criterion for the nominal descriptor system is originally derived and expressed as one compact form of strict and complex linear matrix inequality (LMI). Then, the result can be extended to cope with the specific stability region for the uncertain fuzzy descriptor systems with integrating multiple derivative matrices. Moreover, since the presented criteria involve complex LMIs, we appropriately conduct a projection scheme, where current LMI tools cannot evaluate them. By deriving useful projection operators onto the formed convex sets, an analysing algorithm is consequently presented for numerical evaluation. Finally, three numerical examples, two nonlinear systems and a physical circuit system, are given to demonstrate the validity and the practicability of the proposed approach.