The Output Feedback H∞ Control Design for the Linear Stochastic System Driven by Both Brownian Motion and Poisson Jumps: A Nonlinear Matrix Inequality Approach

We extend the output feedback H_∞ control approaches to the stochastic system including Poisson jumps. In this model, both the control and exogenous disturbance simultaneously enter the volatility and jumps. By completing square methods, a nonlinear matrix inequality is used for solving such problems to give the necessary and sufficient conditions for the existence of a compensator.