This paper investigates the problem of finite-time \(H_2/H_\infty\) static output feedback (SOF) control for discrete-time stochastic Markovian jump systems (MJSs) subject to parametric uncertainties. Initially, by constructing a Lyapunov–Krasovskii functional and fully accounting for the characteristics of MJSs, new sufficient conditions for the existence of a robust finite-time \(H_2/H_\infty\) controller for closed-loop system (C-LS) are derived. Subsequently, a SOF finite-time \(H_2/H_\infty\) controller is designed using a novel linear matrix inequality approach. This controller not only ensures robust \(H_2/H_\infty\) finite-time boundedness but also aims to minimize the upper bound of the \(H_2\) performance index for the C-LS. Three case studies–two numerical simulations and a pest population control application–are provided to validate the effectiveness and practicality of the proposed approach.
