A Unified Approach for Input–Output Finite-Time Mean Square Stabilization of Nonlinear Stochastic Markovian Jump Systems With Poisson Noise

This paper investigates the input-output finite-time mean-square (IO-FTMS) stabilization problem for nonlinear stochastic Markovian jump systems subject to both Wiener and Poisson noises. To break through the traditional IO-FTMS stability confined to single disturbance type (either$W\_{2}$or$W\_\infty$), a new IO-FTMS stability analysis framework is proposed, which simultaneously encompasses both$W\_{2}$and$W\_\infty$disturbance signals. On this basis, by introducing a piecewise time-varying parameter function$\delta (T)$, less conservative unified IO-FTMS stability conditions are established. In addition, the unified IO-FTMS stabilizing controller is designed via the completion of squares method for decoupling, and an algorithm is proposed to determine the feasible domain of parameters ($\alpha$,$\beta$). Finally, an example validates the effectiveness of the proposed approach.