Robust LPV-based infinite horizon LQR design

In this paper, the problem of robust infinite horizon linear quadratic regulator (LQR) design is addressed for uncertain affine linear parameter-varying (LPV) systems. The proposed method extends the standard infinite horizon LQR design to LPV-based static output-feedback (SOF), dynamic output-feedback (DOF) and to a well known proportional, integral and derivative (PID) controller design for uncertain affine LPV systems. The optimal (suboptimal) controller design is formulated as an optimization problem subject to some linear/bilinear matrix inequality (LMI/BMI) constraints. As the main result, the suggested performance and stability conditions, without any restriction on the controller and system structure, are convex functions of the scheduling and uncertainty parameters. Hence, there is no need for applying multi-convexity or other relaxation techniques and consequently the proposed solution delivers a less conservative design method. The viability of the novel design technique is demonstrated and evaluated through numerical examples.