Finite-time asynchronous H∞ control for Markov jump singularly perturbed systems with partially known probabilities

•In this paper, H∞ finite-time stability and boundedness are first applied to discrete-time MJSPSs with partially known probability information. Compared with other existing literature, it guarantees the boundedness in the finite-time region of MJSPSs, but not the state convergence in the infinite interval.•The HMM is adopted to solve the difficulty where system modes are inconsistent with controller modes, and a situation where obtaining probabilistic information is not easy is analyzed based on the HMM. It considers that partially known probability information exists in the transition probability matrix of Markov chain, or in the observation probability matrix, or in both. It is more comprehensive and practical than the case of the completely known probability information.•The conditions for the existence of the finite-time asynchronous H∞ controller are presented, and the design method of the controller is proposed by solving the linear matrix inequalities independent of SPP. Finally, two examples are given to verify the effectiveness and practicability of the proposed method.