Static Output Feedback Linear Quadratic Regulator Design: A Constrained State-Feedback Approach

Abstract This article addresses the problem of static output feedback (SOF) linear quadratic regulator (LQR) design by proposing a novel approach that eliminates the need for an initial stabilizing gain, a common bottleneck in existing methods. By deriving necessary and sufficient conditions for SOF stabilizability using the state-feedback gain landscape, we transform the SOF problem into a constrained state-feedback LQR problem. This time-dependent LQR problem is reformulated as a matrix optimization problem and solved using a modified version of the augmented Lagrangian method (mALM). The mALM incorporates a switched gradient descent approach with Hessian-based step sizes for faster convergence. Our method is validated through example studies and benchmark comparisons, demonstrating its robustness and computational efficiency against state-of-the-art algorithms.