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Reducing conservatism in robust stability analysis of fractional-order-polytopic systems

Abolpour, R ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.1016/j.isatra.2021.02.044
  3. Publisher: ISA - Instrumentation, Systems, and Automation Society , 2022
  4. Abstract:
  5. This paper studies the robust stability of the fractional-order (FO) LTI systems with polytopic uncertainty. Generally, the characteristic polynomial of the system dynamic matrix is not an affine function of the uncertain parameters. Consequently, the robust stability of the uncertain system cannot be evaluated by well-known approaches including LMIs or exposed edges theorem. Here, an over-parameterization technique is developed to convert the main characteristic polynomial into a set of local over-parameterized characteristic polynomials (LOPCPs). It is proved that the robust stability of LOPCPs implies the robust stability of the uncertain system. Then, an algorithm is proposed to explore system's robust stability through investigating the robust stability of these LOPCPs based on the exposed edges idea. For the sake of feasibility comparison, extensive examples are elaborated that reveal the superiority of the proposed algorithm. © 2021 ISA
  6. Keywords:
  7. Exposed edges theorem ; Fractional-order systems ; Over parameterization ; Polytopic systems ; Linear systems ; Parameterization ; Polynomials ; Robustness (control systems) ; Uncertain systems ; Uncertainty analysis ; Characteristic polynomials ; Fractional order ; Parameterization techniques ; Polytopic system ; Polytopic uncertainties ; Robust stability ; Robust stability analysis ; Uncertain parameters ; System stability
  8. Source: ISA Transactions ; Volume 119 , 2022 , Pages 106-117 ; 00190578 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0019057821001270