Abstract
This paper concentrates on the robust control and maximal bound analysis of uncertainty for the LTI fractional order system (FOS), which is subjected to poly-topic and H-infinity bounded uncertainties with 0 <; α <; 1. Firstly, two problems including robust stability analysis and stabilization are investigated. Subsequently, the method of how to determine the maximal uncertainty bound of such system is discussed, and the corresponding linear state feedback stabilizing controller is obtained together. The conditions in terms of linear matrix inequalities (LMI) for these problems mentioned above are concluded as four theorems. Finally, the advantage of the proposed methods is illustrated by two numerical examples.
Highlights
Recently, researchers have found that the dynamical behavior of many physical systems in real world could be described with the fractional calculus more completely and elegantly [1], such as biological systems, viscoelastic systems, economic systems, electrochemistry, and chaos [2]–[4]
In [29], [30], the necessary and sufficient conditions for the stability and stabilization of fractional order system (FOS) with interval uncertainty are presented based on linear matrix inequalities (LMI), for the 1 < α < 2 case and 0 < α < 1 case, respectively
This paper has solved the robust stabilization and maximal uncertainty bound determination problem for the LTI-FOS with two types of uncertainties, which are poly-topic and H -infinity bounded uncertainties
Summary
Researchers have found that the dynamical behavior of many physical systems in real world could be described with the fractional calculus more completely and elegantly [1], such as biological systems, viscoelastic systems, economic systems, electrochemistry, and chaos [2]–[4]. In [29], [30], the necessary and sufficient conditions for the stability and stabilization of FOS with interval uncertainty are presented based on LMI, for the 1 < α < 2 case and 0 < α < 1 case, respectively. In [32], the problems of stability and stabilization for FOS subjected to poly-topic and H2 norm bounded uncertainties are investigated. It is clearly that only one type of uncertainty is considered in most studies, poly-topic and interval uncertainties, ploy–topic and H2 norm bounded uncertainties are considered simultaneously in [31] and [32], respectively This manner generalizes the scope of uncertainty and covers larger number of FOS. In is the identity matrix of order n, · denotes the symmetric structure in matrix
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