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Journal ArticleDOI

Fractional-Order Vectorial Halanay-Type Inequalities With Applications for Stability and Synchronization Analyses

01 Mar 2023-IEEE transactions on systems, man, and cybernetics (IEEE transactions on systems, man, and cybernetics)-Vol. 53, Iss: 3, pp 1573-1583
TL;DR: In this article , the integer-order vectorial Halanay-type inequality is further extended to fractional-order ones in both time-invariant and time-varying forms.
Abstract: The Halanay inequality is widely used in various time-delayed dynamical systems analyses and its vectorial form has become available recently. In this article, the integer-order vectorial Halanay-type inequality is further extended to fractional-order ones in both time-invariant and time-varying forms. It is shown that the fractional-order vectorial Halanay-type inequalities hold under the derived conditions in the form of $M$ -matrices. In addition, the time-invariant inequalities are applied to analyzing the stability and synchronization of fractional-order systems with two numerical examples to substantiate the theoretical results.
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01 Mar 2022
TL;DR: In this article , a necessary and sufficient condition for the robust D-stabilization of the closed-loop control system based on the zero exclusion condition and the value set concept is introduced.
Abstract: This article focuses on the robust D-stabilization analysis of fractional-order control systems where each of the system and the controller may be of fractional order. The coefficients of the system are considered as complex linear functions of interval uncertain parameters, so this article deals with fractional-order polytopic systems. First, a necessary and sufficient condition is introduced for the robust D-stabilization of the closed-loop control system based on the zero exclusion condition and the value set concept. Then, the geometric pattern of the value set of the characteristic polynomial is obtained analytically using the exposed vertices. Second, a function is presented to check the introduced condition. Third, the transition points, at which the exposed vertices of the value set may change, are derived to reduce the computational burthen. Fourth, a new function is provided to determine the D-stability robustness radius (margin) of these control systems, that is, determining bounds on the uncertain parameters such that the control system remains D-stable. The achieved results are applicable to systems of incommensurate order and consequently of commensurate order. Finally, numerical simulations and practical experiments based on a three-degrees-of-freedom flight simulator turn table are conducted to illustrate the achieved results.

3 citations