Robust Stability of Fractional-Order Linear Time-Invariant Systems: Parametric versus Unstructured Uncertainty Models. (23rd August 2018)

• Record Type: Journal Article
• Authors: Matušů, Radek; Şenol, Bilal; Pekař, Libor
• Other Names: Elwakil Ahmed Academic Editor.
• Is Part Of: Complexity. Volume 2018(2018)
• Publication Date: 2018-08-23
• Subjects: Chaotic behavior in systems -- Periodicals; Complexity (Philosophy) -- Periodicals; 003
• DOI: 10.1155/2018/8073481
• Languages: English
• ISSNs: 1076-2787

Abstract

Abstract : The main aim of this paper is to present and compare three approaches to uncertainty modeling and robust stability analysis for fractional-order (FO) linear time-invariant (LTI) single-input single-output (SISO) uncertain systems. The investigated objects are described either via FO models with parametric uncertainty, by means of FO unstructured multiplicative uncertainty models, or through FO unstructured additive uncertainty models, while the unstructured models are constructed on the basis of appropriate selection of a nominal plant and a weight function. Robust stability investigation for systems with parametric uncertainty uses the combination of plotting the value sets and application of the zero exclusion condition. For the case of systems with unstructured uncertainty, the graphical interpretation of the utilized robust stability test is based mainly on the envelopes of the Nyquist diagrams. The theoretical foundations are followed by two extensive, illustrative examples where the plant models are created; the robust stability of feedback control loops is analyzed, and obtained results are discussed.