Linear-Quadratic-Gaussian control of fractional-order systems based on delta vs. nabla fractional-order difference

The paper presents two ways of modeling fractional-order systems using delta and nabla definitions of Grünwald-Letnikov fractional-order difference. Finite-length approximation of fractional-order system are then applied for designing a linear-quadratic-estimator of fractional-order system. Predicted state-space vector are used by linear-quadratic-regulator. That approach enables simple determination of standard integer-order LQG controller for control of fractional-order system. The simulation experiments confirm that presented methodology is efficient and enables obtaining a good controller performance.