The paper proposes a method for structured state-feedback controllers design for linear time-invariant systems. A necessary and sufficient condition for structured state-feedback stabilizability of linear systems, making an appeal to the linear-quadratic (LQ) regulator theory, is first proposed. The latter is presented in the form of a nonlinear matrix equation. Then, it is recast as a nonsmooth unconstrained equation using projection onto the positive semi-definite matrices cone. Thereby, a nonsmooth Newton’s iterative algorithm, based on the Clarke generalized Jacobian of said projection, is proposed. This method has a guaranteed local convergence. Finally, numerical examples illustrate the effectiveness of the proposed method.

提出了一种用于线性时不变系统的结构化状态反馈控制器设计方法。首先提出了线性系统的结构化状态反馈稳定性的必要和充分条件，从而吸引了线性二次（LQ）调节器理论。后者以非线性矩阵方程的形式表示。然后，使用投影到正半定矩阵圆锥上，将其重铸为非光滑无约束方程。因此，提出了一种基于所述投影的克拉克广义雅可比行列式的非光滑牛顿迭代算法。该方法具有保证的局部收敛性。最后，数值算例说明了该方法的有效性。