LPV/Polytopic Stabilization Control and Estimation in Robotics

Nonlinear robotic systems often operate under widely varying conditions that challenge traditional linear control approaches. The Linear Parameter-Varying (LPV) paradigm overcomes these limitations and offers a unifying framework by representing the system’s time-varying dynamics as a convex blend of linear models. This enables both controller and observer synthesis through convex optimization, while considering nonlinearities and time-dependent behavior. This paper presents a linear matrix inequality (LMI)-based methodology for simultaneous stabilization control and state estimation in robotic application within the LPV/polytopic setting. Parallel to controller design, the full-state estimation challenge posed by limited sensors in robotics is addressed. An LPV observer architecture, based on the Luemberger observer, is proposed. The simultaneous observer/controller gains synthesis is then reduced to an LMI feasibility problem. The efficacy of our approach is then demonstrated and illustrated through simulations.