Abstract
The interval model plays an important role in parametric robust control. This paper deals with the strict positive realness of a class of composite interval control systems, and establishes a strong Kharitonov-like extreme point criterion. We also discuss the robust strict positive realness of the shifted interval plant-controller family, and improve some previous results in the literature. Furthermore, for the collection of Popov plots of an interval transfer function family, we prove that a large portion of its outer boundary comes from the sixteen Kharitonov transfer functions. Finally, we study the beta boundedness of interval systems. A strong Kharitonov-like vertex result is established, namely, that all members in the interval system family are beta bounded if and only if the sixteen Kharitonov critical vertices are beta bounded.
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Wang, L. Composite Interval Control Systems: Some Strong Kharitonov-Like Properties. Reliable Computing 6, 231–246 (2000). https://doi.org/10.1023/A:1009974328506
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DOI: https://doi.org/10.1023/A:1009974328506