Low-order H∞ controller design for discrete-time linear systems

We consider the H_∞ control problem for discrete-time linear systems via low-order dynamic output feedback controllers. The existence condition of desirable controllers is expressed as a feasibility problem of a bilinear matrix inequality (BMI) with respect to a coefficient matrix variable defining the controller and a Lyapunov matrix variable. To solve the BMI, we propose two sufficient conditions which result in LMIs, by using a block diagonal structure of the Lyapunov matrix variable.