Intelligent digital redesign revisited: Approximate discretization and stability limitation

Abstract

This paper sharpens the recently developed intelligent digital redesign (IDR) technique in regard of stability. A major assumption in the previous result was that the firing strength of each fuzzy rule is approximated as its sampled value during a sampling period for efficient discretization of the Takagi–Sugeno (T–S) fuzzy system, by which some unexpected stability might be experienced for certain sampling period as large as the assumption is unrealistic. To clarify results for that case, we refine the IDR condition and prove that the uniformly semiglobal practical asymptotic stability of the sampled-data T–S fuzzy control system by the intelligently redesigned digital fuzzy controller, rather than the global exponential stability shown in the previous result.