Admissibilization for Implicit Jump Systems With Mixed Retarded Delays Based on Reciprocally Convex Integral Inequality and Barbalat's Lemma

This article considers admissibility analysis and stabilization for implicit Markovian jump systems (IMJSs) with retarded discrete-distributed delays. Admissibility analysis is investigated for the unforced delay IMJSs by virtue of reciprocally convex integral inequality technique and Barbalat's lemma. State feedback controller is designed via the matrix transformation technique to realize the stabilization of the delayed closed-loop IMJSs. By selecting comprehensive L-K functional with modes and delays information, admissibilization conditions are presented in terms of LMIs. Two illustrative examples including an inverted pendulum controlled by a direct current motor (DCMCIP) system are utilized to certify the effectiveness and practicality of the admissibilization technique.

Automated summary

This article examines admissibility analysis and stabilization for implicit Markovian jump systems with retarded discrete-distributed delays, utilizing a novel state feedback controller design approach to achieve stability for the systems.