Improved mixed H2/H? robust fault-tolerant control against sensor failures

For a class of polytopic uncertain systems, the problem of robust fault-tolerant control against sensor faults is presented. By using of Linear Matrix Inequality (LMI) relaxation technique, a matrix inequality representation is given to guarantee the system stability and mixed H₂/H_∞ performance. A new sufficient and necessary condition for the existence of mixed H₂/H_∞ robust fault-tolerant controller is derived based on parameter-department Lyapunov function. The condition eliminates the coupling of Lyapunov variable and system matrices by introducing slack variable to reduce the conservatism of controller design. The nonlinear matrix inequality in the proposed condition is converted into LMI about new variables based on variable substitution method. A numerical example is given to demonstrate the effectiveness of the approach.