Investigation of robust stability for fractional-order LTI systems with multilinear structure of ellipsoidal parametric uncertainty

The contribution focuses on the investigation of robust stability for fractional-order linear time-invariant (LTI) systems with the multilinear structure of ellipsoidal parametric uncertainty, i.e., the analyzed family of fractional-order polynomials has the multilinear uncertainty structure and an ellipsoid-shaped uncertainty bounding set. The robust stability test is based on the numerical calculation and subsequent plot of the value sets, and the application of the zero exclusion condition. Unlike the previously published works, this contribution shows that, contrary to the case of a two-dimensional ellipse of parameters, the internal points of a three-dimensional ellipsoid of parameters cannot create the boundary of the value set in the complex plane even under more complicated uncertainty structures, such as the multilinear one. © 2020, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

Calculation of robustly stabilizing PI controllers for linear time-invariant systems with multiplicative uncertainty

The contribution is intended to present a method of computing robustly stabilizing PI controllers for linear time-invariant systems with unstructured multiplicative uncertainty. This graphical technique is based on the application of basic robust stability condition and plotting the robust stability border pairs of P-I parameters, which subsequently leads to the robust stability region. The illustrative example is presented to show the effectivity of this straightforward approach. © Springer Nature Switzerland AG. 2019.MSMT-7778/2014, MŠMT, Ministerstvo Školství, Mládeže a Tělovýchovy; LO1303, MŠMT, Ministerstvo Školství, Mládeže a TělovýchovyMinistry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [LO1303 (MSMT-7778/2014)

Value sets of ellipsoidal polynomial families with affine linear uncertainty structure

The contribution focuses on the value sets of the ellipsoidal polynomial families with affine linear uncertainty structure. First, it recalls the fundamental terms from the area of robustness under parametric uncertainty, such as uncertainty structure, uncertainty bounding set, family, and value set, with emphasis to the ellipsoidal polynomial families. Then, the illustrative example is elaborated, in which the value sets of the ellipsoidal polynomial family with affine linear uncertainty structure are plotted, including randomly chosen internal points, and compared with the value sets of the classical “box” version of the polynomial family. © Springer Nature Switzerland AG 2019.Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [LO1303 (MSMT-7778/2014)