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This paper is concerned with the problems of finite-time stochastic <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> control for singular Itô Markovian jump systems with <inline-formula> <tex-math notation="LaTeX">$(x,v)$ </tex-math></inline-formula>-dependent noise and generally uncertain transition rates (GUTRs). Based on two equivalent sets, a new criterion, ensuring the considered systems with completely known TRs to be finite-time stochastically bounded with <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> performance, is first established, which is less conservative than the existing one. Then, the obtained results are extended to the case of GUTRs. To overcome the nonlinear difficulty resulting in the Young inequality for designing a convex controller, an approach called the association of free variables and slack variables are used. The state feedback controller and observer-based controller are respectively designed such that the corresponding closed-loop systems with GUTRs are finite-time stochastically bounded while achieving <inline-formula> <tex-math notation="LaTeX">$H_\infty $ </tex-math></inline-formula> performance. Finally, the numerical examples are addressed to illustrate the effectiveness and efficiency of our obtained results.

Finite-Time Stochastic $H_\infty$ Control for Singular Markovian Jump Systems With $(x,v)$ -Dependent Noise and Generally Uncertain Transition Rates