Decentralized H_∞ controller design for descriptor systems

The authors consider a decentralized H_∞ control problem for multichannel linear time-invariant (LTI) descriptor systems. The aim is to design a low-order dynamic output feedback controller. The control problem is reduced to a feasibility problem of a bilinear matrix inequality (BMI) with respect to variables of a coefficient matrix defining the controller, a Lyapunov matrix, and a matrix related to the descriptor matrix. There is no globally effective method for solving general BMIs. In this article, under a matching condition between the descriptor matrix and the measurement output matrix (or the control input matrix), the authors propose to set the Lyapunov matrix in the BMI as block diagonal appropriately so that the BMI is reduced to LMIs.