1. Institute of Robotics and Automatic Information System, Nankai University, Tianjin 300071, China 2. Tianjin Key Laboratory of Intelligent Robotics, Nankai University, Tianjin 300071, China 3. College of Sciences, Northeastern University, Shenyang 110819, China 4. Shenzhen Research Institute of Nankai University, Shenzhen 518083, China
In this paper, observer-based control for fractional-order singular systems with order α (0 < α < 1) and input delay is studied. On the basis of the Smith predictor and approximation error, the system with input delay is approximately equivalent to the system without input delay. Furthermore, based on the linear matrix inequality (LMI) technique, the necessary and sufficient condition of observer-based control is proposed. Since the condition is a nonstrict LMI, including the equality constraint, it will lead to some trouble when solving problems using toolbox. Thus, the strict LMI-based condition is improved in the paper. Finally, a numerical example and a direct current motor example are given to illustrate the effectiveness of the strict LMI-based condition.
