Low order H∞ controller design: An LMI approach

In this paper, we consider the H
∞
controller design problem for both continuous-time and discrete-time linear time-invariant (LTI) systems via low order dynamic output feedback controllers. The existence condition of desired H
∞
controllers is expressed as a feasibility problem of a bilinear matrix inequality (BMI) with respect to a coefficient matrix defining the controller and a Lya-punov matrix. To solve the BMI, we propose two sufficient conditions which result in linear matrix inequalities (LMIs), by using a block diagonal structure of an equivalent matrix of the Lyapunov matrix in the BMI.