| Abstract: | ![]()
This paper focuses on the H∞ model reduction problem of positive fractional order systems. For a stable positive fractional order system, we aim to construct a positive reduced‐order fractional system such that the associated error system is stable with a prescribed H∞ performance. Then, based on the bounded real lemma for fractional order systems, a sufficient condition is given to characterize the model reduction problem with a prescribed H∞‐norm error bound in terms of a linear matrix inequality (LMI). Furthermore, by introducing a new flexible real matrix variable, the desired reduced‐order system matrices are decoupled with the complex matrix variable and further parameterized by the new matrix variable. A corresponding iterative LMI algorithm is also proposed. Finally, several illustrative examples are given to show the effectiveness of the proposed algorithms. |
