# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
LMI-based robust control of fractional-order uncertain linear systems. (English) Zbl 1228.93087
Summary: We are concerned with the method of observer-based control and static output feedback control for fractional-order uncertain systems with the fractional commensurate order $\alpha$($0<\alpha <1\right)$ and $\alpha$($1\le \alpha <2\right)$ via linear matrix inequality (LMI) approach, respectively. First, the sufficient conditions for robust asymptotical stability of the closed-loop control systems are presented. Next, by using matrix’s singular value decomposition (SVD) and LMI technics, the existence condition and method of designing a robust stabilizing controller for such fractional-order control systems are derived. Unlike previous methods, the results are obtained in terms of LMI, which can be easily obtained by Matlab’s LMI toolbox. Finally, two numerical examples demonstrate the validity of this approach.
##### MSC:
 93D05 Lyapunov and other classical stabilities of control systems 34A08 Fractional differential equations 93C42 Fuzzy control systems
Matlab