Finite-Dimensional Sampled-Data Control of Fractional-Order Systems

In this letter, we address the design of a finite-dimensional control law based on sampled-data for a class of linear continuous-time fractional-order systems. Using the proposed finite-dimensional controller which only requires a finite number of previous control inputs to compute the current control signal, input-to-state stability (ISS) is established for the corresponding closed-loop systems by considering the hereditary and infinite memory properties of the fractional-order systems. A sufficient condition for determining the control signal storage space is also provided to guarantee certain control performance. Numerical simulations illustrate the effectiveness of the proposed design methods and validate the theoretical results.