Abstract: The problem of dissipative fuzzy control for singular Markovian jump systems is studied with generally uncertain transition rates. Firstly， a new Lyapunov-Krasovskii functional is established to develop the new bounded real lemma (BRL) which guarantee the system to be stochastically admissible with given dissipative performance α. Delay decomposition approach and new inequality to deal with functional are used， which can reduce the conservatism to a certain extent. Secondly， based on these ingredients， the explicit expression of the desired controller is obtained by solving a set of strict linear matrix inequalities (LMIs). In the design process of the controller， the generally uncertain transition rates are divided into two cases， and then obtain the LMIs in two different cases. Finally， some numerical examples reflect the less conservatism and effectiveness of the method in this article.

Key words: singular systems; Markovian jump systems; dissipativity; fuzzy control; generally uncertain transition rates