Observer-based controller design for uncertain singular fractional-order systems via LMI approach

This paper considers singular fractional-order systems with order 0 < alpha < 1. Necessary and sufficient condition of designing an observer-based controller for the closed-loop systems to be admissible is obtained. The approach is derived via linear matrix inequalities (LMIs) and two cases for certain and uncertain system are discussed respectively. Meanwhile, we can design a state feedback controller which keeps the system admissible through this approach. Furthermore, two examples for certain and uncertain singular system are given to demonstrate the effectiveness of the results respectively. And the state figures are obtained through simulink toolbox to verify the feasibility of the designed observer-based controller.