In this paper, the non-fragile \(H_{\infty }\) controller design problem for a class of nonlinear singular Markovian jump systems (SMJSs) with time-varying delay and generally uncertain transition rates is considered. We construct a new Lyapunov-Krasovskii functional (LKF) containing double integral terms, by decomposing the integral interval and introducing the free weight matrices, new sufficient conditions on singular stochastic finite-time boundedness (SSFTB) and singular stochastic \(H_{\infty }\) finite-time boundedness (SS \(H_{\infty }\) FTB) of the closed-loop (C-L) SMJSs are derived. Then, a non-fragile finite-time \(H_{\infty }\) controller is designed to ensure the SS \(H_{\infty }\) FTB of the C-L systems with strict LMIs, although existing the controller gain perturbations. Finally, a numerical example and two practical examples of DC motor model and aircraft propulsion system model are provided to illustrate the effectiveness and feasibility of the method.
