Performance analysis and control of fractional‐order positive systems.

Unlike a general integer‐order linear system, the L1 and L2 norms of its state and output variables may not be convergent in an infinite time interval even if the concerned fractional‐order linear system is asymptotically stable or even Mittag–Leffler stable. Therefore, this study mainly investigates the analysis and synthesis of L1 and L2 performances in a finite time interval for a class of fractional‐order positive systems. The L∞ performance problem in the infinite time interval is also concerned since the boundness of the L∞ norm of the state and output variables can be guaranteed in the infinite time interval if the concerned fractional‐order positive system is asymptotical stable. The L1 and L∞ performance characterisations are expressed by linear programming and L2 performance characterisation is expressed in terms of linear matrix inequality with a diagonal positive definite solution. Based on these performance conditions, the problems of stabilisation by a state feedback controller with Lp(p∈{1,2,∞}) ‐gain guaranteed are solved for fractional‐order positive systems. An example is presented to show the effectiveness of the proposed methods in this study. [ABSTRACT FROM AUTHOR]