M-matrix based robust stability and stabilization for uncertain discrete-time switched TS fuzzy systems with time-varying delays

Abstract

This paper provides novel sufficient conditions on robust asymptotic stability and stabilization for a class of uncertain discrete-time switched fuzzy with time-varying delays. The attention is focused on developing new algebraic criteria to break with classical criteria in terms of Linear Matrix Inequalities (LMIs). Firstly, based on the M-matrix proprieties and through l1,∞ induced norms notion, new delay-dependent sufficient conditions are derived to ensure the asymptotic stability and stabilization for a class of uncertain discrete-time switched fuzzy systems with time-varying delay. Secondly, these results are extended for a class of uncertain discrete-time switched fuzzy systems with time delays, modeled by difference equations. Finally, two numerical examples and practical example (a robot arm) are provided to demonstrate the advantage and the effectiveness of our results.

Keywords: Fuzzy control; Induced norms; M-matrix; Polytopic uncertainties; Stability; Switched TS fuzzy system; Time-varying delays.