Bounded-input bounded-output (BIBO) stability of distributed-order linear time-invariant (LTI) systems with uncertain order weight functions and uncertain dynamic matrices is investigated in this paper. The order weight function in these uncertain systems is assumed to be totally unknown lying between two known positive bounds. First, some properties of stability boundaries of fractional distributed-order systems with respect to location of eigenvalues of dynamic matrix are proved. Then, on the basis of these properties, it is shown that the stability boundary of distributed-order systems with the aforementioned uncertain order weight functions is located in a certain region on the complex plane defined by the upper and lower bounds of the order weight function. Thereby, sufficient conditions are obtained to ensure robust stability in distributed-order LTI systems with uncertain order weight functions and uncertain dynamic matrices. Numerical examples are presented to verify the obtained results.
Robust Stability Analysis of Distributed-Order Linear Time-Invariant Systems With Uncertain Order Weight Functions and Uncertain Dynamic Matrices
Sharif University of Technology,
Tehran 1458889694, Iran
Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received June 27, 2016; final manuscript received June 12, 2017; published online August 28, 2017. Assoc. Editor: Yunjun Xu.
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Taghavian, H., and Saleh Tavazoei, M. (August 28, 2017). "Robust Stability Analysis of Distributed-Order Linear Time-Invariant Systems With Uncertain Order Weight Functions and Uncertain Dynamic Matrices." ASME. J. Dyn. Sys., Meas., Control. December 2017; 139(12): 121010. https://doi.org/10.1115/1.4037268
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