On extension of a gradient-based co-design algorithm to linear descriptor systems

As a holistic approach, optimal co-design of a control system determines both the plant and controller simultaneously to optimize certain performance metrics. Prior co-design work typically assume a control system in the classic state space form, and thus compromise the range of applicability. This paper considers co-design for control systems in the linear descriptor form, with the purpose to minimize the H
₂
norm of a closed-loop transfer function. We demonstrate that the gradient of the cost function with respect to plant parameters can be computed analytically, and thus extend the previous gradient-based co-design algorithm to the linear descriptor system case.