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 W₂ or W_∞), a new IO-FTMS stability analysis framework is proposed, which simultaneously encompasses both W₂ and W_∞ disturbance signals. On this basis, by introducing a piecewise time-varying parameter function δ(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 (α, β). Finally, an example validates the effectiveness of the proposed approach.